Question

Please help<3

What is the length of SR?

9 units
12 units
15 units
18 units

Answer 1

From ΔRTQ :

cos (RQT) = TQ / RQ = 16/20 = 4/5 = 0.8

∴ sin (RQT) = √(1-sin²(RQT)) = 0.6

∴ tan (RQT) = sin (RQT)/ cos (RQT) = 0.6/0.8 = 0.75 ⇒⇒⇒ (1)

But
tan (RQT) = SR/RQ ⇒⇒⇒ (2)

From (1) and (2):

∴ SR/RQ = 0.75
∴ SR = 0.75 * RQ = 0.75 * 20 = 15
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Another solution:
------------------------
∵ ΔSRQ is a right triangle
and RT⊥SQ

RT =
`√(RQ^2 - TQ^2)`
∴ RT =
`√(20^2 - 16^2)` = 12
And
RT² = ST * TQ
∴ ST = RT² / TQ = 12²/16 = 9
∴ SR =
`√(ST^2 + TR^2)`
∴ SR =
`√(9^2 + 12^2)` = 15
==============================================================
Another solution:
------------------------
∵ ΔSRQ is a right triangle
and RT⊥SQ

RQ² = QT * QS
∴ QS = RQ²/QT = 20²/16 = 400/16 = 25

∴ SR =
`√(SQ^2 - RQ^2)`
∴ SR =
`√(25^2 - 20^2)` = 15