Question

In a right-angled triangle, it is given that A is an acute angle and that tan A = `3/4`. Without using tables, find the value of cos A.

Answer 1

Given: In a right-angled triangle, A is acute and tan A = `3/4`.

Step-wise calculation:

1. Let opposite = 3k and adjacent = 4k

So, tan A = `"Opposite"/"Adjacent"`

= `3/4`

2. Hypotenuse = `sqrt((3k)^2 + (4k)^2)`

= `sqrt(9k^2 + 16k^2)`

= `sqrt(25k^2)`

= 5k

3. cos A = `"Adjacent"/"Hypotenuse"`   ...(A is acute ⇒ cosine positive.)

= `(4k)/(5k)`

= `4/5` 

cos A =` 4/5`