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  • 12-12-2019
  • Mathematics
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In ΔRST, the measure of ∠T=90°, the measure of ∠S=66°, and ST = 2.2 feet. Find the length of TR to the nearest tenth of a foot..

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calculista
calculista calculista
  • 17-12-2019

Answer:

[tex]TR=4.9\ ft[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle TRS

The tangent of angle ∠S is equal to divide the opposite side to angle ∠S (TR) by the adjacent side to angle ∠S (TS)

so

[tex]tan(S)=\frac{TR}{TS}[/tex]

we have

[tex]\angle S=66^o\\TS=2.2\ ft[/tex]

substitute

[tex]tan(66^o)=\frac{TR}{2.2}[/tex]

solve for TR

[tex]TR=(2.2)tan(66^o)[/tex]

[tex]TR=4.9\ ft[/tex]

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