Question

In ΔABC, angle C is 90° then find the value of sin (A + B).

Answer 1

Given:

Triangle ABC with angle C = 90°

Formula:

Sum of angles in a triangle is 180° and sin(90°) = 1

Solution:

A + B + C = 180°  [Sum of interior angles of a triangle is 180°]

A + B + 90° = 180°  [Substituting the given value of angle C]

A + B = 180° − 90°  [Transposing 90° to the right side]

A + B = 90°  [Subtracting 90° from 180°]

sin(A + B) = sin(90°)  [Taking sine on both sides]

sin(A + B) = 1  [Using the standard trigonometric value sin(90°) = 1]

∴ sin(A + B) = 1