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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
