How do i find pq in the triangle below?

PQ = 27

Step-by-step explanation:

How to get PQ involves SOH-CAH-TOA.

When you're given a side of a right triangle and an angle on that triangle, you can use SOH-CAH-TOA to find another side. In this instance, you're given the side opposite of the angle and you're looking for PQ, the side adjacent to the angle (the one that's not the hypotenuse). Opposite/Adjacent is associated with tangent. Here's how to set it up:

tan(angle) = opposite/adjacent.

tan(30) = (9√3)/x

From here, it's algebra.

(9√3)/tan(30) = x

Plug into the calculator and x = 27.

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