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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 15 Page 537

Determine the trigonometric ratio to use according to the given information and the unknown.

18.7

Practice makes perfect

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

Note that the given side is opposite the given angle, and the side we want to find is the hypotenuse. Therefore, we will use the sine ratio. sin θ = Length of leg opposite toθ/Length of hypotenuse In our triangle, we have that θ =40^(∘) and the length of the opposite leg is 12. We want to find the length of the hypotenuse.

sin θ = opposite/hypotenuse

SubstituteValues

Substitute values

sin 40^(∘) = 12/x

▼

Solve for x

LHS * x=RHS* x

sin 40^(∘) * x = 12

.LHS /sin 40^(∘).=.RHS /sin 40^(∘).

x = 12/sin 40^(∘)

Use a calculator

x=18.66868...

Round to 1 decimal place(s)

x≈ 18.7