Question

A photographer on the ground watches a hot air balloon rise straight up from a point on the ground that is 100 m

away.
a. What is the vertical height of the balloon when the photographer’s line of sight makes a 62° angle with the
ground? Round your answer to the nearest meter.

Answer 1

The vertical height of the balloon when the photographer's line of sight makes a 62° angle with the ground can be calculated using the tangent function and is approximately 188 meters after rounding to the nearest meter.

Step-by-step explanation:

The student's question involves calculating the vertical height of the balloon given that the photographer's line of sight makes a 62° angle with the ground. This problem can be solved using trigonometry, specifically the tangent function, which relates the angle of a right-angled triangle to the ratio of the opposite side to the adjacent side.

To find the vertical height (h), we can set up the equation using the tangent of the angle:

tan(62°) = h / 100m

By rearranging the equation to solve for h, we get:

h = 100m * tan(62°)

After calculating h using the tangent of 62°, we round the answer to the nearest meter:

h ≈ 188 meters (rounded to nearest meter)