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3 years ago

A scale drawing of a field is shown below. The drawing uses a scale of 1 in. = 14 ft. What is the area of the actual field?

Mathematics

1 answer:

svp [43]3 years ago

3 0

Answer:

D. 4,704 ft²

Step-by-step explanation:

Giving a scale of 1 in. = 14 ft, to find the actual area of the field represented by the triangular drawing above, convert the length of the base and height to the actual lengths of the field using the scale.

Height of drawing = 8 in.

Actual height = 8*14 = 112 ft

Base of drawing = 6 in.

Actual base = 6*14 = 84 ft

Area of the field = area of ∆

Area = ½*base*height

Area = ½*84*112

Area = 4,704 ft²

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<h3>Laws of cosines </h3>

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b^2 + c^2 - a^2)/2bc

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Now, given that the triangle is equilateral, with each of the side lengths equal to s

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cos B = (s^2 + s^2 - s^2)/(2s×s)

cos B = (s^2 )/(2s^2)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

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∴ C = cos⁻¹(0.5)

C = 60°

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A = 60°, B = 60° and C = 60°

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Learn more on The law of cosines here: brainly.com/question/2866347

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