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scZoUnD [109]
2 years ago
14

A triangular parcel of land has 117 meters of frontage, and the other boundaries have lengths of 75 meters and 95 meters. What a

ngles does the frontage make with the two other boundaries? (Round your answers to one decimal place.)
° (smaller value)


° (larger value)
Mathematics
1 answer:
Anna35 [415]2 years ago
7 0

Applying the Law of Cosines, the measure of the angles that the frontage will make with the two other boundaries are: 39.8° and 86.1°.

<em><u>Recall:</u></em>

  • Law of Cosines is given as: c² = a² + b² - 2ab(Cos C)

The triangular parcel is shown in the diagram attached below.

  • Where:

a = 75 m

b = 117 m (frontage)

c = 95 m

∠A and ∠C represents the angles made with the two other boundaries.

Apply the Law of Cosines to solve for ∠A and ∠C.

<em><u>Find ∠A using a² = c² + b² - 2cb(Cos A):</u></em>

  • Plug in the values

75² = 95² + 117² - 2(95)(117)(Cos A)

5,625 = 22,714 - 22,230(Cos A)

5,625 - 22,714 = -22,230(Cos A)

-17,089 = -22,230(Cos A)

  • Divide both sides by -22,230

0.7687 = Cos A\\\\A = cos^{-1}(0.7687)\\\\A = 39.8

<em><u>Find ∠B using b² = a² + c² - 2ac(Cos B):</u></em>

  • Plug in the values

117² = 75² + 95² - 2(75)(95)(Cos B)

13,689 = 14,650 - 14,250(Cos B)

13,689 - 14,650 = -14,250(Cos B)

-961 = -14,250(Cos B)

  • Divide both sides by -14,250

0.0674 = Cos B\\\\B = cos^{-1}(0.0674)\\\\B = 86.1

Therefore, applying the Law of Cosines, the measure of the angles that the frontage will make with the two other boundaries are: 39.8° and 86.1°.

Learn more about the Law of Cosines on:

brainly.com/question/12150768

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