Question

Given the right triangle ABC with right angle B, angle A is twice the size of angle C. If the measure of side AB is 7 units, what is the measure of side AC?

Answer 1

AC= 14 units

Explanation:

Given

`\angle B = 90^\circ` --- right-angled

`AB = 7`

`\angle A = 2\angle C`

Required

Find AC

The question is illustrated using the attached triangle

The angles in a triangle are:

`\angle A + \angle B + \angle C = 180`

Substitute
`\angle B = 90^\circ` and
`\angle A = 2\angle C`

`2\angle C + 90 + \angle C = 180`

Collect like terms

`2\angle C + \angle C = 180 - 90`

`3\angle C = 90`

`\angle C = 30`

To find AC, we make use of the sine of angle C:

`\sin C = (AB)/(AC)` --- i.e. opposite/hypotenuse

So:

`\sin 30 = (7)/(AC)`

Make AC the subject

`AC= (7)/(\sin 30 )`

`AC= (7)/(0.5)`

`AC= 14`