If cotθ = 8/15, where θ is acute, find sinθ

Correct Answer is : 151715/171715

If cotθ = 8/15, where θ is acute, find sinθ

Correct Answer is : 151715/171715

Test Index

JAMB Mathematics 2010 Paper

Question : 42

Total: 49

If cot

\theta

\frac{8}{15}

, where

\theta

is acute, find sin

\theta

$\frac{8}{17}$
$\frac{15}{17}$
$\frac{16}{17}$
$\frac{13}{17}$

Validate

Solution:

Concept:

The cotangent of an angle is the ratio of the adjacent side to the opposite side in a right triangle. Using these sides, we can find the hypotenuse and then sine.

Explanation:

Since

\cot \theta = \frac{8}{15}

, we have:

\cot \theta = \frac{\text{adjacent}}{\text{opposite}} = \frac{8}{15}

So let the adjacent side be

8

and the opposite side be

15

Using Pythagoras theorem:

\text{hypotenuse}^2 = 8^2 + 15^2

= 64 + 225 = 289

\text{hypotenuse} = \sqrt{289} = 17

Thus,

\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{15}{17}

Answer:

\sin \theta = \frac{15}{17}

, which is option B.

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