Use the right triangle and the given information to solve the triangle:
a = 4, B = 52°, Find b, c and angle A.
The definition for a right triangle states that if one of the angles of a triangle is a right angle 90º, the triangle is called a right-angled triangle.
Answer: ∠A = 38°, b = 5.11 and c = 8.30
From the given data
∠B = 52°
⇒ ∠ A = 90° - 52° = 38° ( using angle sum property of a triangle )
⇒ tan (B) = a / b ( from trigonometric ratios )
⇒ tan ( 52°) = 4 / b ( since ∠B = 52° )
⇒ b = 4 / tan (52°) = 3.125 ( on transposing )
⇒ cos (B) = b / c ( cos x = base / hypotenuse )
⇒ c = b / cos (B) = 5.075