6. The Law of Sines and Law of Cosines
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Determine the trigonometric ratio to be used according to the information that is given.
40
We are given the length of one of the legs and the hypotenuse of a right triangle, and want to find the measure of one of its acute angles ∠ J.
sin J = Opposite/Hypotenuse ⇔ 9/14
The sine of the angle is 914. Now, to isolate m∠ J, we will use the inverse function of sin.
sin J=9/14 ⇔ J=sin ^(- 1)9/14
Let's use a calculator to find the value of sin ^(- 1) 914. First, we will set our calculator into degree mode. To do so, push MODE, select Degree
instead of Radian
in the third row, and push ENTER. Next, we push 2ND followed by SIN, introduce the value 914, and press ENTER.
The measure of ∠ J is about 40.