Question

Find the sine of both angle A and angle B.

A. sin A = 5/13; sin B = 12/13
B. sin A = 12/13; sin B = 5/13
C. sin A = 5/12; sin B = 12/5
D. sin A = 13/5; sin B = 13/12

Answer 1

The correct option is A.

Explanation:

Let the third vertex of the triangle be C and the angle C is 90 degree.

In a right angles triangle, the sine ratio is defined as

`\sin \theta=(perpendicular)/(hypotenuse)=(opposite)/(hypotenuse)`

Using sine ratio,

`\sin A=(BC)/(AB)`

`\sin A=(10)/(26)`

`\sin A=(5)/(13)`

`\sin B=(AC)/(AB)`

`\sin B=(24)/(26)`

`\sin B=(12)/(13)`

Since
`\sin A=(5)/(13)` and
`\sin B=(12)/(13)`, therefore the correct option is A.

Answer 2

sin = opposite/hyp

Sin A = 10/26 = 5/13

Sin b = 24/26 = 12/13

The answer is option A

Hope this helps