Suppose you have a right triangle ABC with m<A = 44, C is a right angle, length of side b = 10. What is the m<B, length of sides a and c?

For a problem such as this we will use trig functions.   We know that sine (represented by sin) is the opposite side divided by the hypotenuse.

So sin 44 = a/c. But notice this doesn't help at all since we have 2 unknowns. But we can use cosine (represented as cos) since cosine is adjacent side divided by the hypotenuse.

So cos 44 = 10/c.

Using a scientific calculator we get 0.7193 = 10/c.

Therefore c = 13.9 (rounded to 1 decimal place)

To get the length of side a we could use Pythagorean theorem. But it's best to not use this because if side c (which we just calculated) is incorrect, then the calculation for the length of side a will be incorrect as well.

sin 44 = a/13.9

Using a scientific calculator we get .6947 = a/13.9.

Therefore a = 9.7 (rounded to 1 decimal place)