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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Trigonometry

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Exercise 30 Page 656

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

23.2

Practice makes perfect

We are given the length of the hypotenuse and the measure of an acute angle of a right triangle. We want to find the length of one of the legs of the triangle.

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 = Length of leg adjacent toθ/Length of hypotenuse In our triangle, we have that θ =34^(∘) and the length of the hypotenuse is 28. We want to find the length of the leg adjacent to the angle.

cos θ = adjacent/hypotenuse

SubstituteValues

Substitute values

cos 34^(∘) = x/28

▼

Solve for x

LHS * 28=RHS* 28

cos 34^(∘) * 28 = x

Rearrange equation

x=cos 34^(∘) * 28

Use a calculator

x=23.21305...

Round to 1 decimal place(s)

x≈ 23.2

Subchapter links

Exercises p.655-659