Question

URGENT 15 POINTS in the following diagram
what is the value of y and the value of z?

Answer 1

see explanation

Explanation:

Using the sine ratio in right Δ ACD and the exact value

sin30° =
`(1)/(2)`

sin30° =
`(opposite)/(hypotenuse)` =
`(AD)/(AC)` =
`(y)/(150)` =
`(1)/(2)` ( cross- multiply )

2y = 150 ( divide both sides by 2 )

y = 75

----------------------------------------------------------------------

Using the tangent ration in right Δ ABD and the exact value

tan60° =
`√(3)`

tan60° =
`(opposite)/(adjacent)` =
`(AD)/(BD)` =
`(y)/(z)` =
`(75)/(z)` =
`√(3)` ( cross- multiply )

`√(3)` z = 75 ( divide both sides by
`√(3)` )

z =
`(75)/(√(3) )` ×
`(√(3) )/(√(3) )` =
`(75√(3) )/(3)` = 25
`√(3)`