Question

What's the answer to this

Answer 1

AC ≈ 17.3 , BC ≈ 5.3

Explanation:

using the tangent ratio in right triangle ACD

tan51° =
`(opposite)/(adjacent)` =
`(AC)/(AD)` =
`(AC)/(14)` ( multiply both sides by 14 )

14 × tan51° = AC , then

AC ≈ 17.3 ( to the nearest tenth )

using the cosine ratio in right triangle ABC

cos72° =
`(adjacent)/(hypotenuse)` =
`(BC)/(AC)` =
`(BC)/(17.3)` ( multiply both sides by 17.3 )

17.3 × cos72° = BC , then

BC ≈ 5.3 ( to the nearest tenth )