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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Cumulative Standards Review

Exercise 11 Page 820

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

1.24 m

Practice makes perfect

We are given the length of the hypotenuse and the measure of an acute angle of a ski ramp, which is a right triangle. We want to find the length of its height.

Note that the given side is the hypotenuse, and the side we want to find is adjacent to the given angle. Therefore, we will use the cosine ratio. cos θ = adjacent/hypotenuse In our triangle, we have that θ =75^(∘) and the length of the hypotenuse is 4.8meters. We want to find the length of the height, which is adjacent to the angle.

cos θ = Adjacent/Hypotenuse

SubstituteValues

Substitute values

cos 75^(∘) = h/4.8

▼

Solve for h

LHS * 4.8=RHS* 4.8

cos 75^(∘) * 4.8 = h

Use a calculator

1.242331...=h

Round to 2 decimal place(s)

1.24≈ h

Rearrange equation

h≈ 1.24

Therefore, we have found that the height of a ski ramp is approximately 1.24meters.