OpenStudy (anonymous):

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.

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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4 years ago
OpenStudy (anonymous):

First, use the Law of Sines to find the measure of angle C: a/sinA = c/sin C 95/sin 38 = 75/sin C

4 years ago
OpenStudy (anonymous):

Cross-multiply, you get 95 sin C = 75(sin 38) So, sin C = [75 sin(380]/95 C = 29.08 degrees.

4 years ago
OpenStudy (anonymous):

So angle B is approx 113 degrees. Now, use Law of Sines to find b (side AC): b/sin B = 95/sin 38

4 years ago
OpenStudy (anonymous):

Cross-multiply, you get 95 sin 113 = b/sin 38 b = (95 sin 113)/sin 38 b = 142

4 years ago
OpenStudy (anonymous):

You need the Law of Sines twice.

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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.

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

Correct, or a/sin A = b/sin B either one is correct...they are both identical to each other.

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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.

4 years ago
OpenStudy (anonymous):

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.

4 years ago
OpenStudy (anonymous):

Thanks a bunch for breaking this down for me

4 years ago
OpenStudy (anonymous):

No problem. Welcome.

4 years ago
OpenStudy (anonymous):

Apparently the answer was 312.1, how is that?

4 years ago
OpenStudy (anonymous):

what ws 312.1?

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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.

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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!

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

Will do!

4 years ago
OpenStudy (anonymous):

Great!

4 years ago