   Chapter 11.CR, Problem 2CR 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

In Review Exercises 1 to 4, state the ratio needed, and use it to find the measure of the indicated line segment to the nearest tenth of a unit. To determine

To find:

The measure of the of the indicated line segment to the nearest tenth of a unit.

Explanation

Procedure used:

In any right triangle ABC with mA=θ we have the following ratios.

sinθ=OppositeHypotenuse

Calculation:

Given:

The above figure is a triangle which has two right angled triangles. Let us name the given triangle as follows.

Thus,

In ABD

mABD=70°,

In  ACD

AC=8 ft.

In the given triangle ABC,

BD=CD=x (say)

From the given figure it is clear that the triangle ABD and triangle ACD are similar since,

Thus,

mABC=mACD=70°

mACD=70°

Thus, in ACD we have the acute angle mACD=70°

Length of the hypotenuse =8 ft

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