Question

What are the exact values of a and b?

Right triangle A B C is shown with labeled sides and one labeled angle. Side A B is the hypotenuse and it is labeled 7. Side B C is the height and it is labeled a. Side C A is the base and it is labeled b. The angle opposite side B C is 30 degrees.
a. a=7/2,b= 7/3/3
b. a=7/2,b=7/3
c.7/3/2,b=7/2
d. a=7/2,b=7/2/2

Answer 1

Use the 30–60–90 ratio: sides are 1 : √3 : 2 for (opposite 30) : (opposite 60) : (hypotenuse). With hypotenuse 7,

a = side opposite 30 = 7/2,
b = side opposite 60 = 7·(√3/2) = (7√3)/2.

None of the answer choices as written match b = (7√3)/2.