Question

What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?

Answer 1

D. 4.9 units, 14.2 units

Explanation:

By working in reverse, doing arctan( small side / big side) we can deduce it to answer D, seeing as

4.9/14.2 ~= 0.34507

`tan^(-1)(0.34507) = 19.04degrees`

Which rounds out to 19degrees in the tenths.

Answer 2

So you have a right angle triangle. You need to use trig for this, as you have two values you can figure out a third.

You know that you have

90 deg. angle
19 deg. angle
Therefor you have 71 deg. angle

sin19 = x/15
15sin19 = x
x = 2.2

Now do Pythagoras c^2-b^2=a^2

a = 14.8

So the sides are 2.2 and 14.8 units long. (If these numbers are wrong tell me and I'll edit answer)