Question

Fill in the blanks in the 30-60-90 triangle below side s has a length of (fill in blank) and side h has the length of (fill in blank)
A. 16√ 3 , 16√ 3
B.4 , 8√ 3
C.4√2 , 4√2
D. 4 , 4√3
E. 16√3 ,5

Answer 1

Do you know the ratio of the lengths of the sides of a 30-60-90 triangle?

Answer 2

no

Answer 3

This is something you should memorize because it's very useful.

Answer 4

Start witht he short leg, the one opposite the 30-deg angle. Call the length of that leg 1. Then the hypotenuse is twice that length, or 2. The long leg, opposite the 60-deg angle, is sqrt(3) long.

Answer 5

Now look in your problem. The hypotenuse in your case is 8.
The short leg is s, so how long is s?

Answer 6

would it be 4

Answer 7

@mathstudent55

Answer 8

Yes. Good, the short leg is half the hypotenuse, so it's 4.
Now, how about the long leg? The long leg is sqrt(3) times the short leg.
Since you already know the short leg is 4, you can easily find the long leg, h.

Answer 9

for ratio, 30 faces x, 60 faces (square root 3) x, 90 faces 2x

Answer 10

would h then be 4, 4square 3 which would make D the right answer?

Answer 11

right