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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Trigonometry

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Exercise 31 Page 656

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

57.2

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 hypotenuse.

Note that the given side is adjacent the given angle, and the side we want to find is the hypotenuse. Therefore, we will use the cosine ratio. cos θ = Length of leg adjacent toθ/Length of hypotenuse In our triangle, we have that θ =63^(∘) and the length of the adjacent leg is 15sqrt(3). We want to find the length of the hypotenuse.

cos θ = adjacent/hypotenuse

SubstituteValues

Substitute values

cos 63^(∘) = 15sqrt(3)/x

▼

Solve for x

LHS * x=RHS* x

cos 63^(∘) * x = 15sqrt(3)

.LHS /cos 63^(∘).=.RHS /cos 63^(∘).

x = 15sqrt(3)/cos 63^(∘)

Use a calculator

x=57.22754...

Round to 1 decimal place(s)

x≈ 57.2

Subchapter links

Exercises p.655-659