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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 21 Page 519

Find an interior angle of the right triangle that is congruent to the given angle of depression.

0.6km

Practice makes perfect

In the right triangle, we are given the length of one of the legs and the angle of depression from the top vertex to the bottom-right vertex. Note that, since they alternate interior angles, the given angle and the one in the bottom-right vertex are congruent.

We want to find the length of the side opposite to the interior angle in the triangle — the one that measures 18^(∘). Recall that the tangent of an acute angle in a right triangle is defined as the ratio of its opposite side to its adjacent side. tan θ = Length of opposite side toθ/Length of adjacent side toθ Let's substitute our values into this equation and solve for x.

tan θ = Length of opposite side toθ/Length of adjacent side toθ

SubstituteValues

Substitute values

tan 18^(∘) = x/2

▼

Solve for x

LHS * 2=RHS* 2

tan 18^(∘) * 2 = x

Use a calculator

0.64983...=x

Rearrange equation

x=0.64983...

Round to 1 decimal place(s)

x≈ 0.6

We found that the value of x, correct to the nearest tenth of a unit, is 0.6 kilometers.

Subchapter links

Lesson Check p.518

Standardized Test Prep p.521

Mixed Review p.521