Question

1. Find the missing side lengths of the special right triangles. Leave your answers as radicals in simplest form 30° 9​

Answer 1

a = 18 units

b = 9√3 units

Explanation:

By applying sine rule in the given triangle,

sin(30°) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

`(1)/(2)=(9)/(a)`

a = 18 units

Now apply cosine rule in the given triangle,

cos(30°) =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

`(√(3))/(2)=(b)/(a)`

`(√(3))/(2)=(b)/(18)`

b =
`(18√(3) )/(2)`

b =
`9√(3)` units