Question

Find c. 60° 30° √6 ft Write your answer in simplest radical form. feet​

Answer 1

2 sqrt(2)

Explanation:

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

cos theta = adj / hypotenuse

cos 30 = sqrt(6)/ c

c cos 30 = sqrt(6)

c = sqrt(6)/ cos 30

c = sqrt(6) / ( sqrt(3) /2)

c = 2 sqrt(6) / sqrt(3)

We cannot have a radical in the denominator

c = 2 sqrt(6) / sqrt(3) * sqrt(3)/sqrt(3)

= 2 sqrt(18)/3

We can simplify the sqrt

c = 2 sqrt(9*2) / 3

c = 2 *3 sqrt(2)/3

= 2 sqrt(2)