Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
3. Rotations
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Exercise 58 Page 567

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

86.6ft

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 other leg.

Note that the given side is opposite the given angle, and the side we want to find is adjacent to the given angle. Therefore, we will use the tangent ratio. tan θ = opposite/adjacent In our triangle, we have that θ =30^(∘) and the length of the opposite leg is 50. We want to find the length of the hypotenuse. Let's substitute these values into the tangent ratio and solve for x.
tanθ = opposite/adjacent
tan 30^(∘) = 50/x
Solve for x
tan 30^(∘) * x = 50
x = 50/tan 30^(∘)
x=86.602540...
x≈ 86.6