SOLUTION: A quadrilateral PQRS has PQ = 18, QR = 50, RS = 45 and diagonal QS = 30. If QS bisects the angle at Q, what is the length of PS?

Question 1190326: A quadrilateral PQRS has PQ = 18, QR = 50, RS = 45 and diagonal QS = 30. If QS bisects the angle at Q, what is the length of PS?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let 2x be the measure of the angle that is bisected; so the measures of angles PQS and RQS are each x. Then

Using the law of cosines on triangle QRS,

[1]

Using the law of cosines on triangle PQS,

[2]

Solve [1] for cos(x) and substitute in [2].

I'll leave it to you to do the calculations....

If you only want the answer, without a chance to learn something from working on the problem, the answer is PS=27.

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