Math Challenge #21: What is the length of BC?

GRE Math Challenge Question #21:

What is the length of BC?

A. 7 
B. 9
C. 10
D. 11
E. None of the choices

Solution with Explanation:

Correct Choice: C ( 10 )

There is no immediately obvious way to find the length of side BC, so let’s see what you can 
infer from the picture. You know two of the angles of Triangle ABC, so you can find the third. You’ll label the third angle x. 37 + 53 + x = 180. 

That means x = 90. So really your triangle looks like this:

You should definitely redraw once you discover the triangle is a right triangle!

Now that you know Triangle ABC is a right triangle, you can use the Pythagorean Theorem 
to find the length of BC. BC is the hypotenuse, so 

(6)^2 + (8)2 = c^2. 
36 + 64 = c^2. 
100 = c^2. 
10 = c. 

The length of BC is 10.

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