Question

Can I please have some help? I don't know how to do question e.

Answer 1

see explanation

Explanation:

Using the exact trigonometric values

cos30° =
`(√(3) )/(2)`, sin30° =
`(1)/(2)` and tan45° = 1

Let the point where the segment from C meets AB be D, then

Using ΔBCD

cos30° =
`(adjacent)/(hypotenuse)` =
`(BD)/(x)` and

`(BD)/(x)` =
`(√(3) )/(2)` ( cross- multiply )

2BD =
`√(3)` x ( divide both sides by 2 )

BD =
`(√(3) )/(2)` x ←

sin30° =
`(opposite)/(hypotenuse)` =
`(CD)/(x)` and

`(CD)/(x)` =
`(1)/(2)` ( cross- multiply )

2CD = x ( divide both sides by 2 )

CD =
`(1)/(2)` x

Using ΔACD

tan45° =
`(opposite)/(adjacent)` =
`(CD)/(AD)` =
`((x)/(2) )/(AD)` = 1 , hence

AD =
`(1)/(2)` x ←

Hence

AB = BD + AD =
`(√(3) )/(2)` x +
`(1)/(2)` x = (
`(√(3)+1 )/(2)` ) x