Question

What’s the exact value?

Answer 1

5/8 (= 0.625)

Explanation:

tan A = sin A / cos A

we have here a triangle that is much bigger than to fit into our snuggly around a norm circle (radius = 1).

so, we could either see it embedded in a circle with a radius of the square root of 89, or surrounding a circle with the radius of 8.

in the first case

`5 = \sin(a) * √(89)`

`8 = \cos(b) * √(89)`

in the second case 5 is already tan A but stretched by the radius 8.

so,

`5 = \tan(a) * 8`

so, in both cases the answer is 5/8.