Question

Need help! It's a question from Some Applications of Trigonometry.​

Answer 1

C

Explanation:

given

AB + BC = 10 ( subtract AB from both sides )

BC = 10 - AB

using the tangent ratio in the right triangle and the exact value

tan30° =
`(1)/(√(3) )` , then

tan30°

=
`(AB)/(BC)`

=
`(AB)/(10-AB)` =
`(1)/(√(3) )` ( cross- multiply )

`√(3)` AB = 10 - AB ( add AB to both sides )

`√(3)` AB + AB = 10 ← factor out AB from each term on the left side

AB(
`√(3)` + 1) = 10 ← divide both sides by (
`√(3)` + 1)

AB =
`(10)/(√(3)+1 )`