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Chapter 4: Problem 61

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
The sine of an acute angle in a right triangle can be calculated using the formula \( \sin(\theta) = \frac{opposite}{hypotenuse} \). Where 'opposite' is the length of the side opposite to the acute angle, and 'hypotenuse' is the length of the hypotenuse.

Step by step solution

01

Identify Right Triangle

The problem mentions that you are dealing with a right triangle. A right triangle is a triangle in which one of the angles is a right (90-degree) angle. In any right triangle, the hypotenuse is the side opposite the right angle, and it is always the longest side.
02

Identify Opposite Side

Identify the side that is opposite to the acute angle for which you are trying to find the sine. The side 'opposite' literally means the side that is across from the angle you are considering.
03

Calculate Sine of the Angle

The sine of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse. Using this, you can compute the sine of the acute angle as \( \sin(\theta) = \frac{opposite}{hypotenuse} \).

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