Architecture 6o163u

THE APPLICATION OF TRIGONOMETRY IN THE DIFFERENT ARCHITECTURAL STRUCTURES

Submitted to: JACKIE BOY ATIENZA

Submitted by: MARY CRYZEL ABARIENTOS SAMUEL ARSUA SOFIA BALAORO JAY BENEDICT M. LABAY Science Technology Engineering Mathematics Section 8

Introduction Trigonometry is a branch of mathematics that’s deals with the various properties of trigonometric functions and its applications to determine the unknown angles and side of a triangle. The word “trigonometry” is composed of two Greek language words – “trigonom” and “metron” where, former means “triangle” and the latter indicates “measure”. Trigonometry is a subject which deals with sides, angles, and triangles. It majorly concerns with the ratio between the sides and angles of a right triangle. Trigonometry gives a huge part of our life, it is used in many ways such as architecture, astronomy, oceanology, physics and more. As you can see, everything that surrounds you used trigonometry to finish it. We are surrounded by different applications of trigonometry on our daily life, but the case is we don’t notice it nowadays. We can’t build a house, bridges, buildings, cars and any other stuffs without the knowledge of trigonometry. Trigonometry is used in surveying and to determine a height and distance of a specific object or structure. Determining the location and the distances and in the fields like nondestructive testing for determining things such as the angle of reflection or refraction of an ultrasound wave in navigation. This branch of mathematics is even used as a diverse fields as mechanical engineering, physics, electrical engineering, astronomy, music, biology and ecology. We can say that one individual can’t see or determine an application of trigonometry in their daily activities but this application of trigonometry is hidden with its background information. Maybe we can see a bridge, a strong and well-built bridge, we can only see a bridge that is used to connect two roads that is lifted, this bridge is a product of trigonometry. Its structure and formation are based on the blueprint where we can see a lot of trigonometric

functions used. Trigonometry makes possible for one individual get an unknown angle or length of a side. Trigonometry is used to find the height of a building, house, tree or even an airplane, trigonometry was also used to find the length of a mountain, especially the mount Everest. They used trigonometry to find its height, and we can say that everyone or human races are now using modern technology but they never forget trigonometry because it is part of the life that is used for everyday life. A lot of things are connected with trigonometry and we need to understand more about trigonometry so that we can say that “Trigonometry plays a huge part of life”. This is a field of mathematics that needs critical thinking, although all mathematics needs critical thinking, but for this, it’s important for us to understand it clearly because this will benefit us in a long run. Since the ancient times, trigonometry is widely used, it has many uses like the astronomy and many others applications. It is not a basic of mathematics but it is the most used concept of mathematics. A lot of field of society was dominated with trigonometry and now as part of everyday life. It has a lot of uses since ancient time and now we have technology, a higher part of technology, trigonometry is still a part of the past, present of future.

Architecture Architecture is from the Latin word architectura, which is formed from the words for architect. The word "architecture" has also been adopted to describe other designed systems, especially in information technology. Architecture is a ion, a vocation, a calling – as well as a science and a business. It has been described as a social art and also an artful science. Architecture must be of the highest quality of design. The word architecture can have many meanings. Depending on the context, architecture can refer to:

1. any man-made building or structure 2. a man-made building or structure that is important, large, or highly creative 3. a carefully designed object, such as a chair, a spoon, or a tea kettle 4. a design for a city, town, park, or landscape 5. the art or science of deg and building buildings, structures, objects, and outdoor spaces 6. a building style or method 7. a plan for organizing space 8. the flow of information on a Web page 9. the planned design of any kind of system 10. a systematic arrangement of information or ideas

Architecture has to do with planning and deg form, space and ambience to reflect functional, technical, social, environmental and aesthetic considerations. It requires the creative manipulation and coordination of materials and technology, and of light and shadow. Often, conflicting requirements must be resolved. The practice of architecture also encomes the pragmatic aspects of realizing buildings and structures, including scheduling, cost estimation and construction istration. Documentation produced by architects, typically drawings, plans and technical specifications, defines the structure and/or behavior of a building or other kind of system that is to be or has been constructed. Architects build our homes, buildings, bridges and any other structures. They are the talented people who have skills of deg, aware of social trends, keen business sense, a solid understanding of building science and the law, as pertains to the practice of architecture. Usually, architects lead a team of specialists including structural, mechanical and electrical engineers, as well as others. The architect must also understand and deal with the building codes and bylaws set out by municipal, provincial and federal governments.

Different Types of Architecture There are different types of architectural structures; 1. Residential Architecture Residential architecture focuses on constructing beautiful private dwellings for homeowners. Many of the world’s most famous examples of beautiful architecture were actually commissioned as private residences for homeowners. 2. Commercial or Public Architecture If you focus on this role, you may specialize in larger ventures for business or government entities, erecting public buildings such as shopping malls, libraries, government facilities, and more. Every public building espouses ideas about how we should live. As an architect of public buildings, you help to instill these concepts in the culture with your work. 3. Industrial Architecture If you are interested in working on industrial projects, I suggest you check into civil engineering as a major instead of architecture. It is true that there is an architectural element to industrial projects. In fact, architecture can be major component of these structures, but they are far more elaborate to design than other types of public or private buildings, because of this, civil engineering is a more appropriate major for industrial projects than architecture. 4. Landscape Architecture This type of architecture focuses on outdoor areas. If you go into this specialized field, you might design park lands, gardens, and lawns surrounding college campus buildings and other public destinations. Landscape architects may also work with homeowners and other private parties to design compelling outdoor

areas. You might even be involved with the development of golf courses or similar recreational spots. 5. Vernacular Architecture Vernacular architecture is a category of based on local needs, construction materials and reflecting local traditions. And it’s good if you love our traditions.

Trigonometry in Architecture Trigonometry plays an important role in architecture, especially when you are making plans for you structure. Architects need to calculate the exact and right angles and length of a side of the intersection of the components to ensure stability and safety. Some instances that can be made by architects are domes, arches, beams and suspension bridges. Architects uses trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles. Architecture still one of the most important and advanced sectors of our society. As an architects plan the design of buildings trigonometry is used to ensure its longevity or aesthetic purposes.

For example, trigonometry is used in architecture to find the height of a building with a given distance from one point to the building, it’s like standing a certain distance from the building. Architects know the distance to the building and the angle which they stand in relation to the top

structure. Using tangle calculations for sines and cosines, the height of the building can be measured. Architect knows how important trigonometry in building and planning structures. One important detail that architect must know is the triangulation, it is important in making structures and resisting lateral forces such as wind bracing. These things tend to preoccupy the structural engineers than the architects, but awareness of the need for such aspects is very important as they can affect the design and the structure.

Uses of Trigonometry in Architecture Architects design houses, buildings and other structures. They not only draw the plans for the building but they also have to make sure the building follows safety codes and they also have to plan the budget for the building. In addition to considering the way these buildings look, they also have to make sure they are safe, functional and economical. So here is where trigonometry comes in. Trigonometry has been used in architecture as early as the Ancient Egypt. Like the pyramid for example, they had to have used the Pythagorean theorem, trigonometry and a simple algebra to build an amazing structure. Trigonometry is used to ensure that the buildings is safely built. Architects use trigonometry to calculate roof slopes, light angles, ground surfaces, structural loads and heights of structures.

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For example, architects have to calculate the exact angles of intersection for components

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of their structure to ensure the stability and safety. Examples of trigonometric use in architecture include arches, domes, beams and suspension bridges.

Architects during the Renaissance measured the width of facades using special tools and angle calculations. Dartmouth reveals illustrations of trigonometric measurements were commonplace in the mid-1500s. Raphael used a tool called a bussola, a com that measured angles to determine distance. The bussola was a forerunner to the modern theodolite. Contemporary architects study classical buildings that still stand to ascertain how masters constructed their buildings. Architects use trigonometry as well as calculus to create structurally sound buildings. Calculus functions evaluate the physical forces a building must tolerate during and after its construction. Typically an architect uses a vast majority of the trigonometric functions to make sure that his or her angles and measurements are correct for his final masterpiece.

The Trigonometric Functions:

Example:

Trigonometry can be used to find the length of a wall. You can solve this by using tangent.

Trigonometry can be used to see how far up would be sine.

something is. The trig ratio you can use

to There are different that can be used in the application of trigonometry in of architecture;

Horizontal ray- it is the ray parallel to the surface of the earth emerging from the eye of the observer. Ray of vision- the ray from the eye of the observer towards the object under observation and can be called ray of sight. Angle of elevation- if the object under the observation is above the horizontal ray ing through the point of observation, the measure of the angle formed by the horizontal ray and the ray of vision is known as angle of elevation. Angle of depression- if the object under observation is below the horizontal ray ing through the point of observation, the measure of the angle formed by the horizontal ray and the ray of vision is called as the angle of depression.

Sample Problem Architecture of Ferris wheel To build a Ferris wheel, Trigonometry is applied, a Ferris wheel is a circle with designated points in the circle as the slots of the ride. It’s important for the architect to know the structure of the Ferris wheel and to ensure the strength and its durability.

To find the distance of every slots from each other, first you need to know the angle of elevation for every slots and then the radius. The elevation of the Ferris Wheel must be considered also, because the slots may touch the ground. The speed of the Ferris is also a component to consider, because the slots gives the weight of the riders the impact will be added.

In finding the length of every slots from each other, you will use the arc length formula, s=Ɵr, From the length of it, the revolution will be based on the speed of the rotation. With its rotation we can apply the trigonometric function to make the function related to its revolution and speed.

Citations http://www.nsaa.ns.ca/about/about-architecture/what-is-architecture-what-is-an-architect/ https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles http://math.tutorvista.com/trigonometry/applications-of-trigonometry.html https://hs-mathematics.wikispaces.com/Trigonometry? responseToken=0aa3905cbbe663432cdb1a813f38c53c3 http://mathstudyclub18.blogspot.com/ http://www.techsling.com/2016/05/trigonometry-uses-importance-daily-life/ http://www.pbslearningmedia.org/resource/d4b1bd75-c10a-401c-8f65138da7e847c4/architecture-career-teacher-background/ http://www.thefreedictionary.com/type+of+architecture