Question

Solve the right triangle

Answer 1

I recommend learning the mnemonic SOHCAHTOA (it's very fun to say!)
Here is what SOHCAHTOA represents.

Sin - Opposite / Hypotenuse (SOH)
Cos - Adjacent / Hypotenuse (CAH)
Tan - Opposite / Adjacent (TOA)

The sine of an angle is the length of the side opposite of the angle divided by the length of the hypotenuse.

Thus, the length of the side opposite of the angle divided by the sine will give us the length of the hypotenuse.

The angle is 46 degrees. The length of the side opposite of the angle is 14. The hypotenuse is c.

$c= \dfrac{14}{\sin{46^o}}$

$\approx 19.46$

The tangent of an angle is the length of the side opposite of the angle divided by the length of the side adjacent to the angle.

Thus, the length of the side opposite to the angle divided by the tangent of the angle will give us the length of the other leg.

The length of the side opposite to the angle is 14. The angle is 46. The unknown length of the side adjacent to the angle is b.

$b=\dfrac{14}{\tan{46^o}}$

$\approx 13.52$

This should be what you are looking for. Enjoy!