Question

A, B & C form the vertices of a triangle.

∠ CAB = 90°,
∠ ABC = 51° and AB = 8.6.
Calculate the length of BC rounded to 3 SF.

Answer 1

BC ≈ 13.7

Explanation:

using the cosine ratio in the right triangle

cos51° =
`(adjacent)/(hypotenuse)` =
`(AB)/(BC)` =
`(8.6)/(BC)` ( multiply both sides by BC )

BC × cos51° = 8.6 ( divide both sides by cos51° )

BC =
`(8.6)/(cos51)` ≈ 13.7 ( to 3 sf )