Exercise 137 Page 697

To find the approximate value of x in the given triangle, we should first determine which trigonometric ratio we should use given the known angle.

The leg labeled x is the opposite side of the given angle. Since we know the hypotenuse and we want to know the opposite side, we have to use the sine ratio. sin θ = Opposite/Hypotenuse ⇒ sin 62^(∘) = x/10 Examining the diagram, we can identify the value of sin 62^(∘). |c|c|c|c| θ& cos θ & sin θ & tan θ 28^(∘) & 0.883 & 0.469 & 0.532 62^(∘) & 0.469 & 0.883 & 1.881 With this information we can substitute sin 62^(∘) with 0.883 and solve for x.

sin 62^(∘) = x/10

Substitute

sin 62^(∘)= 0.883

0.883 = x/10

MultEqn

LHS * 10=RHS* 10

8.83 = x

RearrangeEqn

Rearrange equation

x=8.83