Question

Solve for all three unknowns

I was also hoping for a step by step on how to do this, it’s really confusing me and I just can’t get it.

Answer 1

x= 32.3 (3 s.f.)

θ= 21.8° (1 d.p.)

α= 68.2° (1 d.p.)

Explanation:

Applying Pythagoras' Theorem,

x²= 12² +30²

x²= 144 +900

x²= 1044

Square root both sides:

`x = √(1044)`

x= 32.3 (3s.f.)

`\boxed{ \tanθ = (opp)/(adj) }`

`\tanθ = (12)/(30)`

`θ = \tan^( - 1) ( (12)/(30) )`

θ= 21.801° (3 d.p.)

θ= 21.8° (1 d.p.)

`\tan\alpha = (30)/(12)`

`\alpha = \tan ^( - 1) ( (30)/(12) )`

`\alpha`= 68.2° (1 d.p.)

Alternatively,

α +θ +90°= 180° (∠ sum of triangle)

α +21.801° +90°= 180°

α +111.801°= 180°

α= 180° -111.801°

α= 68.199°

α= 68.2° (1 d.p.)