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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

4. Angles of Elevation and Depression

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Exercise 39 Page 521

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

85.2 m

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 =28^(∘) and the length of the opposite leg is 40m. We want to find the length of the hypotenuse.

sin θ = opposite/hypotenuse

SubstituteValues

Substitute values

sin 28^(∘) = 40/x

▼

Solve for x

LHS * x=RHS* x

sin 28^(∘) * x = 40

.LHS /sin 28^(∘).=.RHS /sin 28^(∘).

x = 40/sin 28^(∘)

Use a calculator

x=85.20217...

Round to 1 decimal place(s)

x≈ 85.2

Subchapter links

Lesson Check p.518

Standardized Test Prep p.521

Mixed Review p.521