Answer:
see explanation
Step-by-step explanation:
(a)
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles from 180° for B
∠ B = 180° - (90 + 63)° = 180° - 153° = 27°
(b)
Using the sine ratio in the right triangle
sin63° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{15}{x}[/tex] ( multiply both sides by x )
x × sin63° = 15 ( divide both sides by sin63° )
x = [tex]\frac{15}{sin63}[/tex] ≈ 16.8 ( to 1 dec. place )
(c)
Using the tangent ratio in the right triangle
tan63° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{15}{y}[/tex] ( multiply both sides by y )
y × tan63° = 15 ( divide both sides by tan63° )
y = [tex]\frac{15}{tan63}[/tex] ≈ 7.6 ( to 1 dec. place )
