McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
2. Surface Areas of Prisms and Cylinders
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Exercise 53 Page 821

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

x≈ 8.1

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 =67^(∘) and the length of the opposite leg is 19. We want to find the length of the leg adjacent to the angle.
tan θ = opposite/adjacent
tan 67^(∘) = 19/x
Solve for x
tan 67^(∘) * x = 19
x = 19/tan 67^(∘)
x=8.065021 ...
x≈ 8.1