Question

In angle abc, angle c is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. A=3 c=19

Answer 1

This is a right angled triangle.

C = 90°, c =19, c =Hypotenuse

A = ?, a = 3

By Pythagoras' Theorem:

a² + b² = c²

3² + b² = 19²

9 + b² = 361

b² = 361 - 9

b² = 352

b = √352

b ≈ 18.76


Using Sine A = Opposite / Hypotenuse

Sin A = 3/19 ≈ 0.1579

A =Sin⁻¹(0.1579)

A ≈ 9.09°

Sum of angles in a triangle =180

A + B + C = 180

9.09 + B + 90 =180

B + 99.09 =180

B =180 - 99.09

B = 80.91

A ≈ 9.09°, B ≈ 80.91°, b ≈ 18.76

Hope this helps.