Find the missing value to the nearest hundredth. sin ________ =8/15
To find the missing value, we need to find the angle whose sine is 8/15.
sin(angle) = opposite/hypotenuse = 8/15
Using the Pythagorean theorem, we can find the missing side as follows:
hypotenuse^2 = opposite^2 + adjacent^2
15^2 = 8^2 + adjacent^2
225 = 64 + adjacent^2
225 - 64 = adjacent^2
161 = adjacent^2
adjacent = √161
Now, we can find the missing value using the arctan function:
sin(angle) = 8/15
angle = sin^(-1)(8/15)
angle ≈ sin^(-1)(0.533333)
angle ≈ 32.35 degrees
Therefore, the missing value is approximately 32.35 degrees to the nearest hundredth.