Question

A weather balloon is sighted from points a and b, which are 7.00 km apart on level ground. The angle of elevation of the balloon from point a is 29.0°, and its angle of elevation from point b is 48.0°.

(a) Find the height (in m) of the balloon if it is between points a and b. (Round your answer to three significant digits.)
a) 1645 m
b) 2523 m
c) 2921 m
d) 3487 m
(b) Find its height (in m) if point b is between point a and the weather balloon. (Round your answer to three significant digits.)
a) 2007 m
b) 2769 m
c) 3154 m
d) 3926 m

Answer 1

To find the height of the balloon between points a and b, use the tangent function. The height of the balloon is approximately 3390 m. To find the height of the balloon if point b is between point a and the balloon, use the tangent function again. The height is approximately 5290 m.

Step-by-step explanation:

To find the height of the balloon between points a and b, we can use trigonometry. Let's call the height of the balloon h. We can use the tangent function to set up an equation: tan(29°) = h / 7.00 km. Solving for h, we get h = 7.00 km * tan(29°).

Plugging in the values, we get h ≈ 3.39 km. Converting this to meters, we find that the height of the balloon is approximately 3390 m.

Now, to find the height of the balloon if point b is between point a and the weather balloon, we can use the same trigonometric approach. Setting up the equation using the tangent function, we have tan(48°) = h / 7.00 km. Solving for h, we get h = 7.00 km * tan(48°).

Plugging in the values, we find that h ≈ 5.29 km. Converting this to meters, we get an approximate height of 5290 m.