Question 5 The angle of elevation to the top of a Building in New York is found to be 10 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Round to the tenths. Hint: 1 mile $=5280$ feet Your answer is feet. Question Help: Video Message instructor Submit Question

Step 1 ：We are given that the angle of elevation to the top of the building is 10 degrees and the distance from the base of the building is 1 mile which is equal to 5280 feet.

Step 2 ：We can use the tangent of the angle of elevation to find the height of the building. The tangent of an angle in a right triangle is defined as the ratio of the opposite side (in this case, the height of the building) to the adjacent side (in this case, the distance to the building).

Step 3 ：Setting up the equation, we get \(\tan(10^\circ) = \frac{\text{height}}{5280 \text{ feet}}\).

Step 4 ：Solving for height, we get \(\text{height} = \tan(10^\circ) \times 5280\).

Step 5 ：Calculating the above expression, we find that the height of the building is approximately 931.0 feet.

Step 6 ：Final Answer: The height of the building is \(\boxed{931.0}\) feet.