Question

Max observes the zoo and the library from a helicopter flying at a height of 400 times square root of 3 feet above the ground, as shown below:

What is the distance between the zoo and the library?

800 feet
600 feet
200 feet
400 feet

Answer 1

if you label the angles, you will see you have a 30-60-90 right triangle on the left
and ans isosceles triangle on the right.

Answer 2

in a 30-60-90, if they give you the side opposite the 60 deg angle, what is the hypotenuse?

Answer 3

do you know or need more help?

Answer 4

help

Answer 5

where is it that your lost?

Answer 6

That is the factoid you need to know to quickly solve this problem

Answer 7

the side opp 30º angle is H/2
the side opposite the 60º angle is sqrt(3)*H/2
they give you this side= 400*sqrt(3)

400*sqrt(3)= sqrt(3)*H/2
can you find H using algebra?

Answer 8

3 years ago
do you understand that in a 30-60-90 triangle, if you know the hypotenuse (longest side, opposite the 90 degree angle) is 800, then you know the shorter leg is 400 (800/2), and the middle leg is 400*sqrt(3)

In this problem they tell you the middle leg is 400*sqrt(3), and you have to figure out the hypotenuse is 800

one way is say 400*sqrt(3)= H*sqrt(3)/2
multiply both sides by 2/sqrt(3):
400*sqrt(3)*2/sqrt(3)= H (because 2/sqrt(3) times sqrt(3)/2 is 1)
of course sqrt(3)/sqrt(3)= 1 so you get 400*2= H or
H=800

finally, you know this leg is also = to the leg between the zoo and library (it is an isosceles triangle-- see picture up above)

Answer 9

so i would just solve 400 times square root of 3 feet?

Answer 10

oh so its 800?!!

Answer 11

your answer is 400

Answer 12

because you divide by 2

Answer 13

Because 600 is when you use 2003√ as the short leg of the large triangle.

See, there are 3 triangles there. The large one, and two smaller ones it is split into. Of the two smaller ones, one is another 30-60-90 that you can use the same sort of rules on.

Answer 14

:) glad to help!

Answer 15

oh ok yeah. thanks