Question

The length of AB is ______.

Options

• `(10 - sqrt3) cm`

• `10(sqrt3 - 1) cm`

• `10sqrt3  cm`

• `10(sqrt3 + 1) cm`

Answer 1

The length of AB is `bbunderline(10(sqrt3 - 1) cm)`.

Explanation:

The total base from the 30° angle to the right-angle is \[\frac{10}{\tan 30^\circ} = 10\sqrt{3}\text{ cm}\]. The base of the smaller 45° triangle is \[\frac{10}{\tan 45^\circ} = 10\text{ cm}\]. The length of AB is the difference between these two base lengths: \[10\sqrt{3} - 10 = 10(\sqrt{3} - 1)\text{ cm}\].