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Please help! What is the tangent of ∠QTR if line PR is tangent to circle T at Q, and TS = 1 cm?

A) TQ
B) UQ
C) TR
D) RQ

Please help! What is the tangent of ∠QTR if line PR is tangent to circle T at Q, and-example-1
User Jujuleder
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1 Answer

7 votes

Answer:

D) RQ

Explanation:

The mnemonic SOH CAH TOA tells you the relation for the tangent of an angle in a right triangle is ...

Tan = Opposite/Adjacent

For angle QTR, the Opposite side is RQ and the adjacent side is TQ Then the tangent is ...

tan(∠QTR) = RQ/(1 cm) = RQ . . . . . for RQ expressed in centimeters

_____

Comment on units

The tangent of an angle is a ratio of two distances, so is a unitless quantity. Strictly speaking, RQ has units of length, so the best you can say is that when RQ is expressed in centimeters, the numerical value of the tangent of the angle is the same as the numerical value of the length of RQ.

User Tishawn
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