Question

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your

answers as radicals in simplest form.

Answer 1

x =10

y = 10 sqrt(3)/ 3

Explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 60 = 5 sqrt(3) / x

x sin 60 = 5 sqrt(3)

x = 5 sqrt(3)/sin 60

x = 5 sqrt(3) / sqrt(3)/2

x = 5*2

x =10

tan theta = opp /adj

tan 60 = x/y

ytan 60 = 10

y = x/ tan 60

y = 10/ sqrt(3)

y = 10/ sqrt(3) * sqrt(3)/ sqrt(3)

y = 10 sqrt(3)/ 3