Question

If sin A = cos B and the measure of angle A is 1.5 times the measure of angle B, find the measure of angle A

Answer 1

`A = 54`

Explanation:

Given

`\sin A = \cos B`

`A=1.5B`

Required

Find A

If
`\sin A = \cos B`

Then:

`A +B = 90`

Substitute
`A=1.5B` in
`A +B = 90`

`1.5B + B = 90`

`2.5B = 90`

Solve for B

`B = (90)/(2.5)`

`B = 36`

Substitute
`B = 36` in
`A=1.5B`

`A = 1.5 * 36`

`A = 54`