   Chapter 11.CR, Problem 13CR 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 13 to 17, use the Law of S i n e s or the Law of C o s i n e s to solve each problem. Angle measures should be found to the nearest degree; distances should be found to the nearest tenth of a unit.A building 50 ft tall is on a hillside. A surveyor at a point on the hill observes that the angle of elevation to the top of the building measures 43 ° and the angle of depression to the base of the building measures 16 ° . How far is the surveyor from the base of the building? To determine

How far is the surveyor from the base of the building.

Explanation

Procedure used:

In any triangle ABC such that

AB=c,

BC=a,

CA=b,

mA=α,

mB=β, and

mC=γ.

The Law of cosines is given by

a2=b2+c2-2bccosα

b2=c2+a2-2cacosβ

c2=a2+b2-2abcosγ

The Law of sines is given by

asinα=bsinβ=csinγ

Calculation:

Given:

Let us name the given figure as follows.

From the above figure we have two triangles having right angle at P.

Thus, in ASP we have

mASP=43°

Also, in BSP

mBSP=16°

BS=x

Then, in ASB we have

mASB=mASP+mPSB

mASB=43°+16°

mASB=59°, and

AB=50 ft.

Also BS=x.

Now, consider the triangle ASP to find the mSAP

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