(SAT Prep) In the figure, what is the length of BC?
A. 25
B. 15
C. 18
D. 22

I got 18 as my answer

Step-by-step explanation:

I made a triangle with the right side by dropping a vertical. Lets call the point straight down from C, E

Then I found the angle of D

sin θ = 5/13

θ = sin-¹(5/13)

θ≅22.619°

Then I found length of DE by

cosθ (remember we know what theta is) = X/13

12cosθ = X

X = 12

The length of DE is 12.

Since AD is 30, and the left side has two right angles we can do

AD - DE to find BC.

30-12 is 18

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x