Question

Solve for all three unknowns

Answer 1

Answer:

x= 32.3 (3 s.f.)

θ= 21.8° (1 d.p.)

α= 68.2° (1 d.p.)

Step-by-step explanation:

Applying Pythagoras' Theorem,

x²= 12² +30²

x²= 144 +900

x²= 1044

Square root both sides:

$x = \sqrt{1044}$

x= 32.3 (3s.f.)

$\boxed{ \tanθ = \frac{opp}{adj} }$

$\tanθ = \frac{12}{30}$

$θ = \tan^{ - 1} ( \frac{12}{30} )$

θ= 21.801° (3 d.p.)

θ= 21.8° (1 d.p.)

$\tan\alpha = \frac{30}{12}$

$\alpha = \tan ^{ - 1} ( \frac{30}{12} )$

$\alpha$= 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.)