Question

Sin θ = 12/37. Find tan θ. Right Triangle Trigonometry.

Answer 1

`\huge\boxed{B.\ (12)/(35)}`

Explanation:

Look at the picture.

We know:

`\sin\theta=(a)/(c)\\\\\tan\theta=(a)/(b)`

We have

`\sin\theta=(12)/(37)\Rightarrow a=12,\ c=37`

Use the Pythagorean theorem.

`a^2+b^2=c^2\\\\12^2+b^2=37^2\\\\144+b^2=1369\qquad|\text{subtract 144 from both sides}\\\\b^2=1225\to b=√(1225)\\\\b=35`

Calculate tangent:

`\tan\theta=(12)/(35)`