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:
[tex]x = \sqrt{1044} [/tex]
x= 32.3 (3s.f.)
[tex]\boxed{ \tanθ = \frac{opp}{adj} }[/tex]
[tex] \tanθ = \frac{12}{30} [/tex]
[tex] θ = \tan^{ - 1} ( \frac{12}{30} )[/tex]
θ= 21.801° (3 d.p.)
θ= 21.8° (1 d.p.)
[tex] \tan\alpha = \frac{30}{12} [/tex]
[tex] \alpha = \tan ^{ - 1} ( \frac{30}{12} )[/tex]
[tex] \alpha [/tex]= 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.)
