Alg2/Trig SAT help - in rectangle PQRS, what is tan of angle PQS
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Alg2/Trig SAT help - in rectangle PQRS, what is tan of angle PQS

[From: ] [author: ] [Date: 12-05-01] [Hit: ]
if tan (QPT) = 1/5, then QT / PQ = 1/5.If tan (TSR) = 1/2, then TR / SR = 1/2.We can know that PQ = SR.PQ could be 5 if QT is 1,......
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It's question #8, and i tried using SOHCAHTOA to find sides of the rectangle, but i didn't get 7/10 :(

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Using SOHCAHTOA,

if tan (QPT) = 1/5, then QT / PQ = 1/5.

If tan (TSR) = 1/2, then TR / SR = 1/2.

We can know that PQ = SR.

PQ could be 5 if QT is 1, or PQ could be 10 if QT is 2, and so on.

Likewise, SR could be 2 if TR is 1, or SR could be 4 if TR is 2, or more relevantly, SR could be 10 if TR is 5. Calling PQ and SR the same length, and the others the correct corresponding lengths, will help us solve the problem.

So, PQ = SR = 10, and QT = 2, and TR = 5. QR = PS = QT + TR = 7.

We want tan (PQS), which is PS / PQ. Now we can know that this is 7 / 10,

because PS = QR = QT + TR = 7,

and PQ = 10.
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