Question

The McDougalls plan to fence a triangular parcel of their land. One side of the property is 75 ft in length. It forms a 38 degree angle with another side of the property, which has not yet been measured. The remaining side of the property is 95 ft in length. Approximate to the nearest tenth the length of fence needed to enclose this parcel of the McDougalls' lot.

Answer 1

Draw a triangle, ABC, where AB = 75, angle A = 38, and BC = 95. You want to find AC to the nearest tenth.

Answer 2

First, use the Law of Sines to find the measure of angle C:

a/sinA = c/sin C

95/sin 38 = 75/sin C

Answer 3

Cross-multiply, you get 95 sin C = 75(sin 38)

So, sin C = [75 sin(380]/95
C = 29.08 degrees.

Answer 4

So angle B is approx 113 degrees.

Now, use Law of Sines to find b (side AC):

b/sin B = 95/sin 38

Answer 5

Cross-multiply, you get

95 sin 113 = b/sin 38

b = (95 sin 113)/sin 38

b = 142

Answer 6

You need the Law of Sines twice.

Answer 7

Okay, I think I follow what your sayin. So the answer then is 142 or I need to do more to it?

Answer 8

Answer is 142.0, but go through each step, so you completely uderstand what I have shown you. Feel free to ask any questions you have.

Answer 9

I thought the law of sines was sin A/a = sin B/b = sin C/c ?

Answer 10

Correct, or a/sin A = b/sin B

either one is correct...they are both identical to each other.

Answer 11

If a/b = c/d, then b/a = d/c.

Answer 12

ohhhhh okay thats the only part i was confused about. thank you for explaining!

Answer 13

If 2/4 = 3/6, then 4/2 = 6/3

Answer 14

But first we needed Law of Sines to find angle C, then we used Law of Sines again to find the length of AC, which is b in the diagram.

Answer 15

We could have not written Law of Sines to find b in one step, as we did not know the measure of angle B. We had two unknows, b and angle B.

Answer 16

Thanks a bunch for breaking this down for me

Answer 17

No problem. Welcome.

Answer 18

Apparently the answer was 312.1, how is that?

Answer 19

what ws 312.1?

Answer 20

when i put in my answer it shows me the correct one, and it said it was 312.1

Answer 21

The final answer we got was b = 142.0. The side AC, the remaining side, is 142.0 ft.

Answer 22

I dont know where you got 312.1 from..show me what you did.

Answer 23

That's not what I got, I put in 142.0 as my answer and hit submit and it told me it was wrong and showed me the right answer, which was 312.1 but I don't understand how

Answer 24

312.1 is impossible! The Answer Key you have is wrong.

Answer 25

We have two sides of a triangle, one is 75 and the other is 95. The third side can never be 312. Becuase from Geometry, we know that the sum of two sides of a triangle must be greater than the third side. 75 + 95 = 170. And 170 is not greater than 312.

Answer 26

Check you answer key. Make sure you are looking at the correct problem's answer.

Answer 27

I don't know, but it counted it wrong. I'm going to message my teacher and ask him how it's 312.1

Answer 28

Message you teacher that it is impossible for three sides of a triangle to be 75, 95, and 312. Straightforward Geometry says that is impossible!

Answer 29

Our mathematics says it is 142.0, and that makes perfect sense for this problem.

Answer 30

I know I'm confused. And mad because that killed my grade on the practice. So im definitely messaging him.

Answer 31

Sure, message him. And get back to me what he said.

Answer 32

Will do!

Answer 33

Great!