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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Trigonometry

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Exercise 33 Page 656

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

17.4

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 opposite the given angle. Therefore, we will use the sine ratio. sin θ = Length of leg opposite toθ/Length of hypotenuse In our triangle, we have that θ =38^(∘) and the length of the hypotenuse is 20sqrt(2). We want to find the length of the leg opposite the angle.

sin θ = opposite/hypotenuse

SubstituteValues

Substitute values

sin 38^(∘) = x/20sqrt(2)

▼

Solve for x

LHS * 20sqrt(2)=RHS* 20sqrt(2)

sin 38^(∘) * 20sqrt(2) = x

Rearrange equation

x = sin 38^(∘) * 20sqrt(2)

Use a calculator

x = 17.41353...

Round to 1 decimal place(s)

x≈ 17.4

Subchapter links

Exercises p.655-659