   Chapter 11.1, Problem 36E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

For Exercises 35 to 38, make drawings as needed.In right △ A B C , γ = 90 ° and β = 55 ° . If AB=20in., finda) a (the length of B C - ) correct to tenths.b) b (the length of A C - ) correct to tenths.c) the area of right △ A B C .

To determine

To find:

a. The length of a.

Explanation

In a right angle triangle,

1) The side PQ, which is opposite to the right angle PRQ is called the hypotenuse.

(The hypotenuse is the longest side of the right triangle.)

2) The side RQ is called the adjacent side of angle θ.

3) The side PR is called the opposite side of angle θ.

Hence, the sine ratio for an acute angle is oppositehypotenuse

Given:

In a right angled triangle ABC,

AB = 20 in, β=55°,γ=90°

Hypotenuse, AC=b.

Let AB be the opposite side of the triangle.

θ=55°

We know that,

sinθ=oppositeHypotenuse

sin 55°=20b

From the table 11

To determine

To find:

b. The length of b.

To determine

To find:

c. The area of the triangle, ABC.

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