Question

The angle between the lines x sin 60° + y cos 60° = 5 and x sin 30° + y cos 30° = 7 is ______ 

Options

• 90°

• 30°

• 60°

• 45°

Answer 1

The angle between the lines x sin 60° + y cos 60° = 5 and x sin 30° + y cos 30° = 7 is 30°.

Explanation:

`theta = tan^-1|(-tan30^circ + tan 60^circ)/(1 + tan30^circ tan60^circ)|`

= `tan^-1|(tan60^circ - tan30^circ)/(1 + tan30^circ tan60^circ)| = 30^circ`