Exercise 19 Page 514

We are given the length of the hypotenuse and the measure of an acute angle of a right triangle. We want to find the length of one of the legs.

Note that the given side is the hypotenuse, and the side we want to find is opposite to the given angle. Therefore, we will use the sine ratio.

sin θ = \frac{Length of leg opposite to θ}{Length of hypotenuse}

In our triangle, we have that

θ = 1 2^{\circ}

and the length of the hypotenuse is

100 .

We want to find the length of the opposite leg to the angle.

sin θ = \frac{opposite}{hypotenuse}

SubstituteValues

Substitute values

sin 1 2^{\circ} = \frac{x}{1 0 0}

▼

Solve for

x

MultEqn

$LHS \cdot 100 = RHS \cdot 100$

sin 1 2^{\circ} \cdot 100 = x

RearrangeEqn

Rearrange equation

x = sin 1 2^{\circ} \cdot 100

UseCalc

Use a calculator

x = 20.79116 \dots

RoundDec

Round to $1$ decimal place(s)

x \approx 20.8