Question

The figure shows a right triangle AEB on a rectangle CBED.

The figure shows a rectangle CBED. The diagonal BD of the rectangle is drawn. The length of side CD is 30 centimeters and the measure of angle BCD is 90 degrees and the measure of angle DBE is 60 degrees. There is a right triangle AEB on the side BE of the rectangle. Triangle AEB has the measure of angle AEB equal to 90 degrees and the measure of angle ABE is 30 degrees.

What is the length of side AD?

69.28 cm

45.32 cm

81.96 cm

94.38 cm

Answer 1

I solved it, but it wasn't one of the answer choices. I got 77.32.

Answer 2

@agentx5 Can you help with this? I'm super busy right now and don't remember my geometry that well.

@svanpatten I haven't done geometry in 3 years. haha

Answer 3

Still there @svanpatten ? might be able to help

Answer 4

Yes.

Answer 5

Let me calculate & see what I find. just a sec..

Answer 6

Getting 69.28

Answer 7

First, do you agree that BDC = 60?

Answer 8

How so?

Answer 9

Agree? :)

Answer 10

I know that BE = 30. Right?

Answer 11

How does it equal 60? haha.

Answer 12

Wow, this is going to take long =) but we'll get there. Okay, BED is a triangle, and angles in a triangle add up to 180. Thus BDE=30. ok?

Answer 13

Still there?

Answer 14

Yeah.

Answer 15

u okay with BDE=30?

Answer 16

I thought you meant the measure of the sides, not the angle haha. Yeah I understand that part. Then that would make BE 30 cm. Right?

Answer 17

Yes, BE is 30cm by fact of it being equal to CD, since they form the sides of the same rectangle. It's good you figured out that.
Now, since BDE=30, BDC=60 since both add up to 90. ok?

Answer 18

And be sketching this as we speak...it really helps :)

Answer 19

Yes.

Answer 20

Wonderful. Now, stay with me here:
Tan60 = BC/30
Agree?

Answer 21

Yes

Answer 22

Perfect. So BC = DE = 30Tan60
ok?

Answer 23

Ok

Answer 24

I got it! Thanks!(:

Answer 25

Wonderful. So you know how the answer gets to 69.28?

Answer 26

I hope you do. You're welcome :)