Question

ABCD is a trapezoid (AD∥ BC). BC = 5 cm, m∠ACD = m∠ABC = 90°, m∠BAC = 30°. Find the length of AD (the picture is not drawn to scale).

Answer 1

`AD=20\ cm`

Explanation:

step 1

Find the length of AC

In the right triangle ABC

`sin(<BAC)=(BC)/(AC)`

we have

`m<BAC=30\°`

`BC=5\ cm`

substitute and solve for AC

`sin(30\°)=(5)/(AC)`

`0.5=(5)/(AC)`

`AC=10\ cm`

step 2

Find the length side AD

In the right triangle ACD

`cos(<CAD)=(AC)/(AD)`

we have

`m<CAD=90\°-30\°=60\°`

`AC=10\ cm`

substitute and solve for AD

`cos(60\°)=(10)/(AD)`

`0.5=(10)/(AD)`

`AD=20\ cm`