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A triangular parcel of land has 117 meters of frontage, and the other boundaries have lengths of 75 meters and 95 meters. What angles does the frontage make with the two other boundaries? (Round your answers to one decimal place.)

° (smaller value)


° (larger value)

Sagot :

akposevictor

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°.

Recall:

  • 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.

Find ∠A using a² = c² + b² - 2cb(Cos A):

  • 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

[tex]0.7687 = Cos A\\\\A = cos^{-1}(0.7687)\\\\A = 39.8[/tex]

Find ∠B using b² = a² + c² - 2ac(Cos B):

  • 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

[tex]0.0674 = Cos B\\\\B = cos^{-1}(0.0674)\\\\B = 86.1[/tex]

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:

https://brainly.com/question/12150768

View image akposevictor
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