Question

Find the missing value and round to the nearest hundredth.

Answer 1

You have to use Trigonometric ratios here. I'll help you with a question, and you try to do the other two.

a. You are given the hypotenuse, and told to figure out the opposite. The trigonometric function that deals with that is sin(x), which is opposite over hypotenuse. So:
$sin(51)= \frac{y}{12}$

Solve for y:
$y = 12sin(51)$

Simplify:
$y = 8.043$

For these problems, you have to remember the ratios Sine, Cosine, and Tangent. An easy way is to make a mnemonic device. A good one that a lot of people use is SohCahToa. Which is Sine (Opposite, Hypotenuse), Cosine (Adjacent, Hypotenuse) and Tangent (Opposite, Adjacent). Remember trigonometry is just a glorified field of ratios of sides to angles. There are many more trigonometric ratios including inverse trigonometric ratios, reciprocal trigonometric ratios, and hyperbolic trigonometric ratios (which show up during differential calculus). But for now, focus on this. Haha.