# Question #b5ab2

##### 3 Answers

#### Explanation:

Construct the point

Using the Pythagorean theorem, we have

The sine of an acute angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. Considering the right triangle

As it is clear that

(There are multiple ways of finding this, including using the inverse sine function or calculating it from a special right triangle, however

Substituting this value in, we have

#### Explanation:

Given

The cartesian co-ordinate of the point A is

If

This relation gives

Replacing

#### Explanation:

Drop a perpendicular from point

From right triangle

Therefore,

from which

Since