Question

The following question find the value of the variables. If your answer is not an integer leave it in simplest radical form

The triangle is not drawn to scale.
Ox=1013, y = 30
Ox= 10, y = 30,13
Ox= 30/3, y= 10
Ox= 30, y = 10.73

Answer 1

option 4

Explanation:

using the sine/ cosine ratios in the right triangle and the exact values

cos30° =
`(√(3) )/(2)` , sin30° =
`(1)/(2)` , then

cos30° =
`(adjacent)/(hypotenuse)` =
`(x)/(20√(3) )` =
`(√(3) )/(2)` ( cross- multiply )

2x = 20
`√(3)` ×
`√(3)` = 20 × 3 = 60 ( divide both sides by 2 )

x = 30

and

sin30° =
`(opposite)/(hypotenuse)` =
`(y)/(20√(3) )` =
`(1)/(2)` ( cross- multiply )

2y = 20
`√(3)` ( divide both sides by 2 )

y = 10
`√(3)`