What do you know from the inverse trigonometric ratios?
See solution.
Practice makes perfect
Let △ ABC the right triangle below with side lengths a, b, and c.
By using any of the three trigonometric ratios we can find the measure either of ∠ A or ∠ B. Since the procedure will be similar, it is enough to show how to find m ∠ B.
Using Sine
Let's begin by finding the sine of ∠ B.
sin B = b/c
Next, by using a calculator we can find the inverse sine of b c and that way we find the measure of ∠ B.
m ∠ B = sin^(-1)(b/c)
Using Cosine
As before, we first find the cosine of ∠ B.
cos B = a/c
By using a calculator we can find the inverse cosine of a c and that way we find the measure of ∠ B.
m ∠ B = cos^(-1)(a/c)
Using Tangent
Finally, we start by finding the tangent of ∠ B.
tan B = a/b
By using a calculator, we can find the inverse tangent of a b and that way we find the measure of ∠ B.
m ∠ B = tan^(-1)(a/b)
