Exercise 29 Page 676

Let's begin with recalling the Law of Sines. If △ ABC has lengths of a, b, and c, and angle measures of A, B, and C, then we can write that the ratios of the sine of an angle to the side opposite this angle are equal.

In our exercise we are asked to find the width of the mouth of the tornado, which we will call x, using the given diagram.

To evaluate the value of x, we will create a proportion using the Law of Sines. sin 26^(∘)/x=sin 44^(∘)/200 Let's solve the equation using cross multiplication.

sin 26^(∘)/x=sin 44^(∘)/200

CrossMult

Cross multiply

200sin 26^(∘)=xsin 44^(∘)

DivEqn

.LHS /sin 44^(∘).=.RHS /sin 44^(∘).

200sin 26^(∘)/sin 44^(∘)=x

RearrangeEqn

Rearrange equation

x=200sin 26^(∘)/sin 44^(∘)

UseCalc

Use a calculator

x=126.2120...

RoundDec

Round to 1 decimal place(s)

x≈ 126.2

The width of the mouth of the tornado is approximately 126.2 feet.