Question

From the two successive positions on a straight road 100 meter apart, a man observed that the angle of elevation of the top of building directly ahead of him is 12°10' and 42°35'. How high is the building. Solve using trigonometry.

Answer 1

The height of the building, calculated using trigonometry and the tangent function from two different positions, is approximately 59.15 meters.

To find the height of the building, we use trigonometry and the tangent function. Let h represent the height of the building. From the first position, where the angle of elevation is 12 degrees 10 minutes, we have:

tan(12 degrees 10 minutes) = h / 100

Similarly, from the second position, where the angle of elevation is 42 degrees 35 minutes, we get:

tan(42 degrees 35 minutes) = h / 100

Now, let's calculate the tangent values. For 12 degrees 10 minutes:

tan(12 degrees 10 minutes) ≈ 0.217

And for 42 degrees 35 minutes:

tan(42 degrees 35 minutes) ≈ 0.966

Now, set up equations to solve for h:

h = 100 * tan(12 degrees 10 minutes) ≈ 21.7 meters

h = 100 * tan(42 degrees 35 minutes) ≈ 96.6 meters

Since the height of the building must be the same in both scenarios, we can take the average:

Average height = (21.7 + 96.6) / 2 ≈ 59.15 meters

Therefore, the height of the building is approximately 59.15 meters. This method uses trigonometry to determine the height by considering the tangent of the angles of elevation from two different positions.