Question

a ballon has an angle of elevation of 54° from a point on the ground. from the point on the ground to the balloon the distance is 250feet. a. how far up in the air is the balloon? b. sketch a diagram thay expains situation​

Answer 1

The balloon is 202.25 feet up in the air.

Explanation:

According to Trigonometric functions

Sin Ф = Perpendicular / Hypotenuse

So putting the values here

Sin (54) = x / 250

x = 202.25 feet

Part 2

For diagram see the attached figure

Answer 2

Answer: 202.25 feet.

Explanation:

You can draw a right triangle based on the information given in the problem, where the hypotenuse is 250 feet and the opposite side is the height of the balloon asked.

Therefore, you can solve it as following:

`sin\alpha=(opposite)/(hypotenuse)`

Substitute values and solve for x, then the result is:

`sin(54\°)=(x)/(250)\\x=250*sin(54\°)\\x=202.25`