At a hot air balloon festival jim watches a hot air balloon rise form a distance of 200 yards.

A:From jims position the ballon seen to hover at angle of elevation of 50 What is the height of the ballon

B:After a while the ballon seems to hover at an angle of 75 how high is it off the ground now

Confused

To solve these problems, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

For problem A, let's denote the height of the balloon as "h". The angle of elevation is given as 50 degrees. We can set up the following equation:

tangent(50) = h / 200

To solve for "h", we can rearrange the equation:

h = tangent(50) * 200

1. Use a scientific calculator to find the tangent of 50 degrees.
2. Multiply the tangent value by 200 to find the height of the balloon.

For problem B, let's denote the new height as "H" and the new angle of elevation as 75 degrees. We can use the same process:

tangent(75) = H / 200

Rearranging the equation:

H = tangent(75) * 200

1. Use a scientific calculator to find the tangent of 75 degrees.
2. Multiply the tangent value by 200 to find the new height of the balloon.