Question

Is this statement true or false?

The sine of an angle in a right triangle is the ratio of the length of the side adjacent to that angle to the length of the hypotenuse.

Answer 1

The sine of an angle in a right triangle is the ratio of the length of the side adjacent to that angle to the length of the hypotenuse.

FALSE.

Explanation:

Given:

Diagram is attached below as

Consider, Δ ABC a Right Angle Triangle at ∠ C = 90°

AB = Hypotenuse

Solution:

In Right Angle Triangle Δ ABC , apply sine identity to angle B we get

`\sin B = \frac{\textrm{side opposite to angle B}}{Hypotenuse}\\`

i.e

The sine of an angle in a right triangle is the ratio of the length of the side OPPOSITE to that angle to the length of the hypotenuse... TRUE

Also For Cosine we have

`\sin B = \frac{\textrm{side Adjacent to angle B}}{Hypotenuse}\\`

The Cosine of an angle in a right triangle is the ratio of the length of the side adjacent to that angle to the length of the hypotenuse. ... True

The sine of an angle in a right triangle is the ratio of the length of the side adjacent to that angle to the length of the hypotenuse. ...FALSE