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DanielleElmas [232]
2 years ago
10

The angle of elevation to the top of a skyscraper is measured to be 2 degrees from a point on the ground 1 mile from the buildin

g. How tall is the skyscraper?
Mathematics
1 answer:
Alex2 years ago
4 0

Answer:

0.034921 miles or 1843774 feet tall

Step-by-step explanation:

Using trigonometric functions we know that x=rcos(\theta) and y=rsin(\theta) where \theta=angle and r is the hypotenuse of the triangle.

First we will calculate the hypotenuse using the x equation, since we know x = 1 mile (distance from the building on the ground) we have:

x=rcos(\theta)\\\\1=rcos(2)\\\\r=\frac{1}{cos(2)} \approx. 1.0061mi

Now we will calculate the height of the building using the y equation and so:

y=rsin(\theta)\\\\y=\frac{1}{cos(2)} \times sin(2) = \frac{sin(2)}{cos(2)}=tan(2)=0.034921mi

The building is 0.034921 miles or approximately 184.3774 feet tall.

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