"A house is built on a triangular plot of land. Two sides of the plot are 160 feet long and they meet at an angle of 85 degrees. If a fence is to be built around the property, how much fencing material is needed?"

Question

11-01-2015
Mathematics

Answered

"A house is built on a triangular plot of land. Two sides of the plot are 160 feet long and they meet at an angle of 85 degrees. If a fence is to be built around the property, how much fencing material is needed?"

Answer :

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2beawriter 2beawriter · Answer 1 · 2015-01-11T20:10:27-05:00

C= 85 degrees
/ \
/ \
a= 160    / \ b= 160
   / \
B /_________\ A
c

What you're looking for is c so you can add a, b, and c together to get the material. To do this you need to use this formula, otherwise known as Law of Cosines:
c^2 = a^2 + b^2 - 2abcosC
c^2 = 25600 + 25600 - (2)(160)(160)(cos85)
c^2 = 51200 - (51200)(cos85)
c^2 = 51200 - (-50400.084)
c^2 = 101600.084
c = 318.749
c + a + b = 638.749 or 639 ft if you're looking for a whole number
Keep in mind this answer is if what you're looking for is the perimeter, please let me know if it's the area you are looking for

ewomazinoade ewomazinoade · Answer 2 · 2022-05-25T06:31:21-04:00

The quantity of fencing material that would be needed for the triangular plot of land is 537.03 feet.

How much fencing material is needed?

The first step is to determine the length of the third side of the fence. The formula that can be used to determine the length of the third side is:

c² = a² + b² - 2abcosC

c² = 160² + 160² - (2 x 160 x 160)cos85

c² = 51,200 - 51200 x0.087

c = √47104

c = 217.03 feet

Total length of fencing material = 160 + 160 + 217.03 = 537.03 feet

To learn more about triangles, please check: https://brainly.com/question/22949981

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