Question

Medal will be awarded to whoever provides best assistance. Geometry help please:
You set up a makeshift greenhouse by leaning a square pane of glass against a building. The glass is 4.5 feet long, and it makes a 30 degree angle with the ground. How much horizontal distance between the building and the glass is there to grow plants? Round to the nearest inch.

Answer 1

I have been working on this question for over half an hour, and still don't understand it.

Answer 2

I'm drawing a diagram right now.

Answer 3

Thank you.

Answer 4

A diagram should help.
If I read this problem correctly, the length of any one side is 4.5 feet.
Could it be that the horiz. space for planting is also 4.5 feet? What other alternatives might there be?

Answer 5

Based on my diagram (I am not entirely sure if it is correct), the hypotenuse is 4.5 feet long.

Answer 6

Here's the diagram, and the hypotenuse is 4.5 feet

Answer 7

I know that I have to use this theorem to find the solution somehow: Hypotenuse = \[2 \times shorter leg\], and \[longer leg = \sqrt{3} \times shorter leg\]

Answer 8

Are you certain that you need to find a hypotenuse here?
Have you come up with a sketch yet?
Label the lengths of the (square) pane of glass.

Answer 9

My sketch is very similar to the one attached above by @wolf1728. I think I have to find the distance of the base of the triangle (x), which is the horizontal distance between the building and the glass).

Answer 10

It forms a 30 -60 - 90 triangle
So the "ground" distance is hypotenuse * sqrt if 3 / 2
= 4.5 * 1.7320508076 / 2
= 3.897114317

Answer 11

Would still like to see your sketch.

If all sides of the glass are 4.5 ft in length, and the angle of elevation is 30 degrees,
which trig function would you use to find the horizontal measurement?

Answer 12

You don't even need trig to solve this

Answer 13

My first solution that I got was 4, because
\[\cos 3 = x \div4.5\]
x = 4.5 \[\cos 30\]
x = 4

Answer 14

I apologize if my understanding is a bit slow. This concept is a bit advanced for me because I am an 8th grader studying 9th grade geometry.

Answer 15

If you want to use trig then
cosine 30 = adj/hyp

adjacent = cosine 30 * hypotenuse
adjacent = 0.86603 * 4.5
adjacent = 3.897135

Answer 16

Thank you; I understand it now.

Answer 17

Okay. As I said if you know the properties of a 30 60 90 triangle, you don't even need to use trig.

Answer 18

I went to trig, because the radicals gave me a headache, but thank you so much for your help.

Answer 19

Okay you are welcome.
If you want to see the properties of a 30 60 90 triangle, then click here:
http://www.1728.org/trig2.htm