Question

Use your knowledge of geometry and trigonometry to express the area, A, of the shaded region in terms of theda. b. Find the measure of theda when A=0.5 square unit or explain why there is no possible value of theca. Give the exact value when possible; otherwise, to the nearest hundredth of a radian.

Answer 1

@Ahlpa_Omega32

Answer 2

Okay just one question before I get started

Answer 3

What grade level is this?

Answer 4

its really 11th grade but I'm in 10th

Answer 5

oh well Im in 9th but i can try to help you

Answer 6

ok do u know how to do it

Answer 7

Well I can try to figure it out but I can't be sure that i will get the answer

Answer 8

ok anything will help

Answer 9

@turqoisetuna please help

Answer 10

I would love to help but I'm only in 10th grade level math currently :/

Answer 11

oh ok

Answer 12

@mathmale can you help her with this problem?

Answer 13

Yeah...I tried figuring it out but I don't think I can solve it....it's to hard for me...sorry I wasn't able to help you in any way..

Answer 14

its ok

Answer 15

@mathmale PLEASE HELP

Answer 16

@mathmale can you help or no?? please say yes

Answer 17

I'm interested, and would like to help, but at the moment I'm tied up helping another person with a lengthy problem. Which of the illustrations you've provided are you interested in focusing on? If I can return within 10 minutes or so, I'll help you; otherwise perhaps I could help you tomorrow morning.

Answer 18

honestly all of them because my teacher gave us this hw and we didn't learn ANYTHING on this except cos theda and all that stuff

Answer 19

Unfortunately, Hayley, you'll need to pick just one of those illustrations as our focus.

Answer 20

ok #1 i guess

Answer 21

I see a rectangle of length 2 with a diagonal drawn from the lower left corner to the upper right corner. Do you?

Answer 22

yes

Answer 23

So we are to find the area of this rectangle, correct? What further info need we in order to do that?

Answer 24

the width

Answer 25

Yes, or, as we could say, the height.

The area of the rect. would be A = Length*Height, right?

Answer 26

yes

Answer 27

We already have the length. It was given. It's 2.
We need to use trig to find the height.
Look carefully at the triangle with longer side = to 2 and angle theta.
Which trig function would you use to relate the height to the angle and the long side (2)?

Answer 28

tangent

Answer 29

correct. For that triangle we have the adjacent side (the side adjacent to the angle theta) equal to 2. We don't know the size of the angle (theta), but we can call it theta.

Write the definition of the tangent function here.

Answer 30

tan= opp/adj

Answer 31

Great, and supposing we wanted to solve that equation for "opp," what would the result be?

Answer 32

x= tan theta 2 = x ?

Answer 33

sorry about =x twice i didn't realize

Answer 34

Multiply both sides of tan= opp/adj by adj. What do you get?

Answer 35

2tantheta=x?

Answer 36

Really nice.
so now you have both the length and the height of the rectangle, don't you
?

Answer 37

yes

Answer 38

i can read what you've written, but would prefer to see x = tan theta (with spaces).

So, with length = 2 and height = 2 tan theta,

What is the area, A, of the rectangle?

Answer 39

4 tan theta units squared?

Answer 40

Wow...you've even remembered to insert units of measurement! Perfect.

Wish I could continue working with you, but for me it's past bed time>

Looking at problem #2, I notice that this is a parallelogram (forgot the exact name for it).
The area is simply length x height, as before, but it's going to be a bit harder to find an expression for the height. thought I'd help you get started by sharing these observations with you.

Answer 41

ok thank you

Answer 42

I went back and took a second look and now think the problem is easier than at first glance.

I will be back on OpenStudy in the morning and if you still have unanswered questions then, may be able to help you.

Good night!

Answer 43

ok thank you