A balloon is flying west of two trigonometry students who are 7 miles apart. The angles of elevation of the two students to the balloon are 15 and 28 degrees. Approximate how high the balloon is flying.

As usual, draw a diagram. It is clear that if the nearer student is x away from the spot under the balloon, then

h/x = tan 28°
h/(x+7) = tan 15°

Eliminate x and you have

h/tan28° = h/tan15° - 7
Now just solve for h

vhj

56.78feet

If the set is 25ft, and angle A is 22.5 degrees, the travel is how many ft?

To approximate the height at which the balloon is flying, we can use the concept of trigonometry. We will use the tangent function to calculate the height.

Let's assume that the height of the balloon is h. We know that the distance between the two students is 7 miles, and the angles of elevation to the balloon from the two students are 15° and 28°.

To start, let's consider the student who has an angle of elevation of 15°. By using the tangent function, we can set up the following equation:

tan(15°) = h / x

Here, x represents the distance between this student and the balloon. Since we know that the distance between the two students is 7 miles, we can find the value of x:

x = 7 - y

Where y represents the distance between the other student and the balloon. We can find y using the concept of supplementary angles. Since the two angles of elevation add up to 180° (15° + 28° = 43°), the distance from the other student to the balloon is:

y = x + 7

Now, we can substitute the values of x and y back into the equation to solve for the height:

tan(15°) = h / (7 - (x + 7))

Simplifying further:

tan(15°) = h / (7 - 2x)

Finally, we can solve for h:

h = tan(15°) * (7 - 2x)

To obtain a numerical approximation, we need to find the value of x that satisfies these equations. Once we have that value, we can substitute it back into the equation for h to find the approximate height of the balloon.