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
Explanation:
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
