CLO 4: Solve problems involving triangles

Topic 4: APPLICATIONS OF TRIGONOMETRY

OVERVIEW

In this module, we are going to discuss the application of trigonometry, the bright and oblique triangles. There are many real-world applications involving these triangles. In some problems, only the sides are given. Sometimes, two vsides and an angle are given. It is necessary to identify which of these laws are to be applied in these problems to solve it easily and correctly.

LEARNING OBJECTIVES

At the end of this module, you should be able to:

1. Solve right triangles, sides, angles and areas.

2. Solve real-life right triangle problems.

3. Solve oblique triangles using Law of Sines and Cosines.

Subtopic: SOLUTION OF RIGHT TRIANGLES

A triangle is composed of six parts, the three sides and three angles. To solve a triangle is to find the unknown parts from the parts that are given. In the case of a right triangle, this can always be done if we have given (besides the right angle) two parts, at least one of which is a side. (Rider)

Obviously, it is shown that in this right triangle ABC, angle C is a right angle. In solving a right triangle, we will use the six trigonometric functions (sin, cos, tan, csc, sec, and cot) and also the Pythagorean theorem. Pythagorean theorem states that c^2 = a^2 + b^2, where a and b are the legs and c is the hypotenuse.

Also, we are going to use the relation A + B + C = 180°. Since it is a right triangle and C = 90°, we can say A + B = 90°.

EXAMPLE:

The height of a radio transmission tower is 70 meters, and it casts a shadow of length 45 meters. Find the angle of elevation of the sun.

SOLUTION:

Given the opposite and the adjacent side, we can solve the angle of elevation of the sun by using tangent function

tan θ =70/45

tan B = 1.556

B = arc tan 1.556

B = 57.265°

REFERENCES

Larson, R. (2016) Algebra and Trigonometry: Real Mathematics, Real People, 7th Edition. USA: Cengage Learning

Moyer, R. and Ayres, F. (2009) Schaum’s Outlines: Trigonometry, 4th Edition. USA: McGraw Hill

Rider, P. (1971) Plane and Spherical Trigonometry. New York: The Maximillian Company

https://www.mathwarehouse.com/triangle-calculator/online.php

PROBLEM SET 4

Reflection on Learning

The fourth topic is in relation to the third topic but in this topic, it is focused on the application of trigonometry which then requires integrating the knowledge about formulas and critical thinking as well. I chose the problem above because I find it difficult as I used most of my time figuring out how to answer that. Luckily, I found it out. To answer this problem, a person must first understand the law of sine and cosine which was stated in the module as well as critical analysis. To be specific, this problem was answered using the equation from the law of sine that plays a huge part in answering the equation. In summary, it is a must to point out the differences between the given values in order to not be flabbergasted by the process in solving the situation.