Question

Could you please solve this?

Answer 1

CD ≈ 9.68 cm

Explanation:

use Pythagoras' identity in right triangle ABC to find BC

then use the sine ratio in right triangle BCD to find CD

BC² + AB² = AC² ( substitute values )

BC² + 3² = 8²

BC² + 9 = 64 ( subtract 9 from both sides )

BC² = 55 ( take square root of both sides )

`√(BC^2)` =
`√(55)` , that is

BC =
`√(55)`

using the sine ratio in Δ BCD

sin50° =
`(opposite)/(hypotenuse)` =
`(BC)/(CD)` =
`(√(55) )/(CD)` ( multiply both sides by CD )

CD × sin50° =
`√(55)` ( divide both sides by sin50° )

CD =
`(√(55) )/(sin50)` ≈ 9.68 cm ( to 3 significant figures )