Question

Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.

Answer 1

u = 2 , v = 1

Explanation:

using the sine and tangent ratios in the right triangle, with exact values

sin60° =
`(√(3) )/(2)` and tan60° =
`(√(3) )/(1)` , then

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

`√(3)` × u = 2
`√(3)` ( divide both sides by
`√(3)` )

u = 2

and

tan60° =
`(opposite)/(adjacent)` =
`(√(3) )/(v)` =
`(√(3) )/(1)` ( cross- multiply )

`√(3)` × v =
`√(3)` ( divide both sides by
`√(3)` )

v = 1

thus u = 2 and v = 1