Question

Given the following information, find the length of the missing side. Leave your answer as a simplified radical.

Answer 1

Given:

A figure of a triangle, AD = 6 and DB = 2.

To find:

The length of AC.

Solution:

In a right angle triangle,

`\cos \theta =(Base)/(Hypotenuse)`

In triangle ACD,

`\cos A =(AD)/(AC)`

`\cos 30^\circ =(6)/(AC)`

`(√(3))/(2)=(6)/(AC)`

`√(3)* AC=6* 2`

`AC=(12)/(√(3))`

`AC=(12)/(√(3))* (√(3))/(√(3))`

`AC=(12√(3))/(3)`

`AC=4√(3)`

Therefore, the length of AC is
`4√(3)` units.