Question

Find x

A - 11 √6 / 4
B - 22 √2
C - 11 √6 / 2
D - 11 √2 / 4

Answer 1

A

Explanation:

using the sine ratio in the right triangle on the left to find the vertical side , h, and the exact value

sin60° =
`(√(3) )/(2)` , then

sin60° =
`(opposite)/(hypotenuse)` =
`(h)/(11)` =
`(√(3) )/(2)` ( cross- multiply )

2h = 11
`√(3)` ( divide both sides by 2 )

h =
`(11√(3) )/(2)`

using the sine ratio in the right triangle on the right and the exact value

sin45° =
`(√(2) )/(2)` , then

sin45° =
`(opposite)/(hypotenuse)` =
`(h)/(x)` =
`((11√(3) )/(2) )/(x)` =
`(√(2) )/(2) }` ( cross- multiply )

x =
`(11√(3) )/(2)` ×
`(√(2) )/(2)` =
`(11√(3(2)) )/(2(2))` =
`(11√(6) )/(4)`