Question

I need some help on this. Not sure how to solve.

Answer 1

Answer:

x = 9

Step-by-step explanation:

This shape is a 30-60-90 triangle, which means that the angles of the triangle are each 30°, 60° and 90°.  Given that the measures of the angles of the triangle are known, as well as one side, we can find the measures of all the other sides (example attached).  A 30-60-90 triangle is special because of the relationship of its sides.  The hypotenuse (directly across from the 90° angle) is equal to twice the length (2x) of the shorter leg, in this case labeled 'x' and directly across from the 30° angle.  The longer leg, across from the 60° angle, is equal to multiplying the shorter leg (x) by √3 or x√3.

Since the measure of the hypotenuse is given at 18, we can set the expression of that side equal to 18 and solve for x:

2x = 18  or x = 9