Radhanath Sikdar, a mathematician and surveyor from India, calculated the height of Mount Qomolangma (Mount Everest) in 1852. While standing a distance of 240 kilometers from the peak, he determined that the height of the mountain was 8839 meters.† (Round your answers to two decimal places.)

(a) What was the measure of the angle of elevation from his position to the peak?

(b) If he would have made his calculation from 80 kilometers closer to the peak, what would have been the measure of the angle of elevation?

To solve this problem, we can use trigonometry and the concept of the angle of elevation.

(a) To find the measure of the angle of elevation from Sikdar's position to the peak, we can use the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle.

In this case, we have the opposite side (the height of the mountain) and the adjacent side (the distance from Sikdar's position to the peak). So, we can use the formula:

tan(angle of elevation) = opposite/adjacent

Given that the opposite side (height of the mountain) is 8839 meters and the adjacent side (distance from Sikdar's position to the peak) is 240 kilometers (which is equal to 240,000 meters), we can plug in these values into the formula to find the angle of elevation:

tan(angle of elevation) = 8839/240000

Now, we can use the arctan function (inverse tangent) to find the angle of elevation:

angle of elevation = arctan(8839/240000)

Using a calculator, we find that the angle of elevation is approximately 2.08 degrees.

(b) If Sikdar had made his calculation from 80 kilometers closer to the peak, we need to recalculate the angle of elevation using the new distance.

In this case, the new distance from Sikdar's position to the peak would be 240,000 meters minus 80,000 meters, which is 160,000 meters.

Using the same formula as in part (a), we can calculate the new angle of elevation:

tan(angle of elevation) = 8839/160000

angle of elevation = arctan(8839/160000)

Again, using a calculator, we find that the new angle of elevation would be approximately 3.24 degrees.

hint...Your right angle triangle uses the tangent ratio (O/A).

b) hint... Your right angle triangle uses the tangent ratio where the adjacent is now 160 m