Question

Given A is acute angle and 13 sin A = 5, evaluate without using tables: `(5 sin A - 2 cos A)/(tan A)`.

Answer 1

Given: A is acute and 13 sin A = 5.

Step-wise calculation:

1. `sin A = 5/13`.

2. `cos A = sqrt(1 - sin^2A)`

= `sqrt(1 - (5/13)^2)`

= `sqrt(144/169)`

= `12/13` positive since A is acute.

3. `tan A = (sin A)/(cos A)` 

= `(5/13)/(12/13)` 

= `5/12`

4. Numerator:

5 sin A – 2 cos A

= `5 xx 5/13 - 2 xx 12/13` 

= `(25 - 24)/13`

= `1/13`

5. Divide by tan A:

`1/13 ÷ 5/12`

= `1/13 xx 12/5`

= `12/65`