If θ is an acute angle and sin θ = 21/25 , then what is the value of tan θ ?

If θ is an acute angle and sin θ = 21/25 , then what is…

If $\theta$ is an acute angle and sin $\theta$ = $\frac{21}{25}$ , then what is the value of tan $\theta$ ?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. $\frac{21}{2\sqrt{46}}$ .

sinθ = 21/25 = Length/Hypotenuse

Base = √(Hypotenuse² - Length²) = √(25² - 21²) = √(625 - 441) = √184 = 2√46

tanθ = Length/Base = 21/2√46

Hence, the value of tanθ is 21/2√46.