Question

5. The horizontal and vertical components
of a force are 8 N and 15 N respectively.
The force is​

Answer 1

Answer ⇒ 17 N.

Explanation ⇒ Let the force be F.

This means,

Fx = FSinθ = 8

Fy = FCosθ = 15

Thus,

Fx/Fy = tanθ

∴ tanθ = 8/15

∴ Sinθ = 8/17 and Cosθ = 15/17

Now,

(Fx)² + (Fy)² = F²

Fy² tan²θ + Fy² = F²

Fy² (Sec²θ) = F²

F² =  225Sec²θ

F = 15Secθ

Now,

F = 15/Cosθ

∴ F = 15/(15/17)

∴ F = 17 N.

Hope it helps.