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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Use the drawing provided to show that the area of the isosceles triangle is A = s 2 sin θ cos θ

Chapter 11.2, Problem 41E, Use the drawing provided to show that the area of the isosceles triangle is A=s2sincos

To determine

To find:

To show that the area of the isosceles triangle is A=s2sinθcosθ by using the following figure,

Elementary Geometry for College Students, Chapter 11.2, Problem 41E

Explanation

Consider the following figure,

Let us put the name for the isosceles triangle ia ABC and altitude is AD¯

We know that BD=DC=base2

Assume that BD=DC=xunits

General formula for cosine ratio and sin ratio is given below,

cosθ=adjacenthypotenuseθ=cos1(adjacenthypotenuse) and sinθ=oppositehypotenuseθ=sin1(oppositehypotenuse)

tanθ=oppositeadjacent

For ΔADB:

From the above figure shows that the s is the value of hypotenuse since it is opposite to right angle.

Then DC is the length of the leg opposite to θ.

Therefore,

cosθ=ADAB=ADsAD=(cosθ)s

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