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Please help<3

What is the length of SR?

9 units
12 units
15 units
18 units

Please help<3 What is the length of SR? 9 units 12 units 15 units 18 units-example-1
User Pinkeen
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6.6k points

1 Answer

7 votes
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
==============================================================
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








User Hellfish
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7.2k points