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Chapter 10: Problem 49

If you are given the lengths of the sides of a right triangle, describe how to find the sine of either acute angle.

Short Answer

Expert verified
To find the sine of either acute angle in a right triangle, identify the side opposite to the angle and the hypotenuse. Then, divide the length of the side opposite the angle by the length of the hypotenuse. This gives the sine of the angle.

Step by step solution

01

Identify sides of the triangle

First, determine which side of the triangle is the hypotenuse (the longest side, opposite the right angle), which side is adjacent to the angle of interest (the side that is one of the sides of the angle), and which side is opposite the angle of interest (the side across from the angle).
02

Apply the sine formula

Next, apply the sine formula. The sine of an angle in a right triangle is given by the ratio of the length of the side opposite the angle to the length of the hypotenuse. This can be formulated as \(sin(\theta) = \frac{opposite}{hypotenuse}\). Replace 'opposite' with the length of the side opposite the angle and 'hypotenuse' with the length of the hypotenuse and calculate the result.
03

Simplify the result

The last step consists of simplifying the result, if possible. If the calculations are correct, the result should be a number between -1 and 1, inclusive.

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Most popular questions from this chapter

Use a calculator to find each of the following: \(\sin 32^{\circ}\) and \(\cos 58^{\circ} ; \sin 17^{\circ}\) and \(\cos 73^{\circ} ; \sin 50^{\circ}\) and \(\cos 40^{\circ} ; \sin 88^{\circ}\) and \(\cos 2^{\circ}\). Describe what you observe. Based on your observations, what do you think the co in cosine stands for?

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Explain the following analogy: In terms of formulas used to compute volume, a pyramid is to a rectangular solid just as a cone is to a cylinder.

What general assumption did Euclid make about a point and a line in order to prove that the sum of the measures of the angles of a triangle is \(180^{\circ}\) ?

In Exercises 15-20, find the measure of the complement and the supplement of each angle. \(1^{\circ}\)
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