Given triangle ABC with ß = 41°, g = 14°, and a = 5.0, find the value of c.
A. 17
B. 6.2
C. 1.5
D. 4.0

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Asked 3/8/2013 8:33:23 PM

Updated 213 days ago|8/1/2023 8:55:41 AM

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Expert answered|iamjasonquines|Points 10|

Question

Asked 3/8/2013 8:33:23 PM

Updated 213 days ago|8/1/2023 8:55:41 AM

1 Answer/Comment

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To find the height of the building, we can use trigonometry. Let's assume the height of the building is "h" feet.

We have two right triangles formed in this scenario:

1. The first right triangle consists of the hill, the building's height "h," and the horizontal ground. The angle of elevation from this point to the top of the building is 15.0°.

2. The second right triangle consists of the hill, the building's height "h," and the distance 75.0 feet from the base of the building. The angle of elevation from this point to the top of the building is 55.0°.

Using trigonometric ratios, we can set up the following equations:

1. tan(15.0°) = h / (distance along the hill)

2. tan(55.0°) = h / 75.0 feet

Now, let's solve for "h" in each equation:

1. h = (distance along the hill) * tan(15.0°)

2. h = 75.0 feet * tan(55.0°)

Using a calculator, we find:

1. h = 20.45 feet

2. h = 84.02 feet

The height of the building is approximately 84.0 feet (rounded to one decimal place), so the correct answer is 84.0 feet.

We have two right triangles formed in this scenario:

1. The first right triangle consists of the hill, the building's height "h," and the horizontal ground. The angle of elevation from this point to the top of the building is 15.0°.

2. The second right triangle consists of the hill, the building's height "h," and the distance 75.0 feet from the base of the building. The angle of elevation from this point to the top of the building is 55.0°.

Using trigonometric ratios, we can set up the following equations:

1. tan(15.0°) = h / (distance along the hill)

2. tan(55.0°) = h / 75.0 feet

Now, let's solve for "h" in each equation:

1. h = (distance along the hill) * tan(15.0°)

2. h = 75.0 feet * tan(55.0°)

Using a calculator, we find:

1. h = 20.45 feet

2. h = 84.02 feet

The height of the building is approximately 84.0 feet (rounded to one decimal place), so the correct answer is 84.0 feet.

Added 213 days ago|8/1/2023 8:55:41 AM

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