Question

Solve the right triangle ABC, with C = 90.00◦ , a = 15.21 cm, b = 17.34 cm. Round to two decimal places.

Answer 1

• the hypotenuse side, c = 23.1 cm

• angle A = 41.26 ⁰

• angle B = 48.74 ⁰

Explanation:

Given;

first leg of the right triangle, a = 15.21 cm

second leg of the right triangle, b = 17.34 cm

Angle C = 90 ⁰

The missing parameters;

• the hypotenuse side = c

• angle A

• angle B

Use Pythagoras theorem to calculate the missing side "c", which is the hypotenuse

c² = a² + b²

c² = (15.21)² + (17.34)²

c² = 532.02

c = √532.02

c = 23.1 cm

The missing angle A is calculated as;

`tan(A) = (a)/(b) \\\\tan(A) = (15.21)/(17.34) \\\\tan(A) = 0.8772 \\\\A = tan^(-1) (0.8772)\\\\A = 41.26^0`

The missing angle is calculated as;

B = 90⁰ - A

B = 90⁰ - 41.26⁰

B = 48.74⁰