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

Answer:

AC= 14 units

Step-by-step 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:

$\sin C = \frac{AB}{AC}$ --- i.e. opposite/hypotenuse

So:

$\sin 30 = \frac{7}{AC}$

Make AC the subject

$AC= \frac{7}{\sin 30 }$

$AC= \frac{7}{0.5}$

$AC= 14$