Question

If tan theta =5/12 then what is the value of sin theta

Answer 1

Answer:

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Answer 2

Given,

tan θ  = 5 / 12

To Find,

sin θ  =?

Solution,

We know from the formula of tan θ  that

tan θ  = Perpendicular / Base

tan θ  = 5 / 12 = Perpendicular / Base

By equating values we get,

Perpendicular   = 5

Base = 12

Using Pythagoras theorem, we get

Hypotenuse ² = Perpendicular ² + Base²

$H^2 = 5^2 + 12^2\\H^2 = 25 + 144\\H^2 = 169\\H = \sqrt{169}\\ H = 13$

Hypotenuse = 13

From the formula of sin θ we know that,

sin θ = Perpendicular / Hypotenuse

sin θ = 5 / 13

Hence, If tan theta =5/12 then the value of sin theta is 5/13.