Question

Please help!!!!
Trigonometry
Find the value of aBc
Compound shape

Answer 1

∠ ABC = 75°

Explanation:

using the sine ratio in right Δ ABD

sin ABD =
`(opposite)/(hypotenuse)` =
`(AD)/(AB)` =
`(4)/(8)` =
`(1)/(2)` , then

∠ ABD =
`sin^(-1)` (
`(1)/(2)` ) = 30°

Using the sine ratio in right Δ CBD

sin CBD =
`(opposite)/(hypotenuse)` =
`(CD)/(BC)` =
`(3)/(3√(2) )` =
`(1)/(√(2) )` , then

∠ CBD =
`sin^(-1)` (
`(1)/(√(2) )` ) = 45°

Then

∠ ABC = ∠ABD + ∠ CBD = 30° + 45° = 75°