Question

Find the value of each variable. If your answer is not an integer, express it in simplest radical form.

Answer 1

a = 15

b = 5(6 - √3)

Explanation:

Construction to be done in the given figure → Drop a perpendicular line (DE) from D to line AB.

From ΔAED,

cos(60°) =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

=
`(AE)/(AD)`

cos(60°) =
`(AE)/(10√(3))`

`(1)/(2)=(AE)/(10√(3))`

AE =
`5√(3)`

Since, b = AB - AE

b = (30 - 5√3)

b = 5(6 - √3)

By sine rule,

sin(60°) =
`\frac{\text{Oppositet side}}{\text{Hypotenuse}}`

`(√(3))/(2)=(a)/(10√(3))`

a =
`(30)/(2)`

a = 15