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?
9 units, 12 units
11 units, 10.2 units
4.9 units, 15.8 units
4.9 units, 14.2 units
5.2 units, 14.1 units

Answer 1

You have one angle that is not the right angle and the length of the hypotenuse. All you need is two basic trigonometric rules to solve this.

Let's call one of the sides x and the other y

Imagine having a triangle with sides x, y and h. Where x is the adjacent and y is the opposite to your 19° angle.

Cosine of any angle is the adjacent over the hypotenuse. So you can write the first equation like this:
[ cos(19°)=x/15 ] now solve for x to get [ x=15cos(19°) ] or about 14.2 units (make sure that your calculator is in degree mode).

The other side of the triangle can be solved similarly by knowing that the sine of any angle is the opposite over the hypotenuse.
[ sin(19°)=y/15 ] and again solve for y to get [ y=15sin(19°) ] or about 4.9 units.

Your answer is D. 4.9 units, 14.2 units

All done.