Question

If `tan theta = 24/7`, find that sin θ + cos θ.

Answer 1

Let x be the hypotenuse.

In Δ ABC, by applying Pythagoras theorem.

AC² = AB² + BC²

x² = (24)² + (7)²

x² = 576 + 49

x² = 625

x = `sqrt(625)`

x = 25

`sin theta = (AB)/(AC) = 24/25`

`cos theta = (BC)/(AC) = 7/25`

∴ `sin theta + cos theta = 24/25 + 7/25`

`= 31/25`