Question

In problem 3, the wind blows harder and the top of the

balloon is now 15 feet over from the stake. What is the
height of the balloon now? Draw a diagram to help you
solve the problem and explain your answer.

Answer 1

To solve this problem, we can use the Pythagorean theorem to find the height of the balloon. In particular, we can consider the right triangle formed by the stake, the top of the balloon, and the part of the string that is attached to the stake.

[asy]

unitsize(2 cm);

pair A, B, C, D, E;

A = (0,0);

B = (0,15);

C = extension(A,B,A+(1,0),B+(1,0));

D = extension(A,C,A+(0,1),C+(0,1));

E = extension(B,D,B+(0,-1),D+(0,-1));

draw(A--B--C--cycle);

draw(A--D--E--cycle);

draw(rightanglemark(A,D,C,2));

label("$A$", A, S);

label("$B$", B, N);

label("$C$", C, E);

label("$D$", D, E);

label("$E$", E, W);

[/asy]

Let $a$ be the distance from the stake to the top of the balloon, $b$ be the height of the balloon, and $c$ be the length of the string. We know that $a = 15$ feet and $c = 15$ feet, so we can use the Pythagorean theorem to find $b$:

$a^2 + b^2 = c^2$

$15^2 + b^2 = 15^2$

$225 + b^2 = 225$

$b^2 = 0$

$b = \sqrt{0} = 0$ feet

Therefore, the height of the balloon is 0 feet. This is because the balloon has been pulled up by the wind so that its top is directly above the stake, and therefore its height is 0 feet.