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A water balloon is being launched into the air at a
73^(@) angle of elevation from the ground. The water balloon reaches a height of 30 feet directly above your head. How far from you was the water balloon launched?

$5$ . A water balloon is being launched into the air at a $73^{\circ}$ angle of elevation from the ground. The water balloon reaches a height of $30$ feet directly above your head. How far from you was the water balloon launched?

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Pythagorean theorem

Full solution

Q.

5

. A water balloon is being launched into the air at a

73^{\circ}

angle of elevation from the ground. The water balloon reaches a height of

30

feet directly above your head. How far from you was the water balloon launched?

Identify Triangle: Identify the triangle formed by the water balloon's path. The height of $30$ feet is the opposite side of the right triangle, and the angle of elevation is $73$ degrees.
Use Tangent Function: Use the tangent function, which relates the opposite side to the adjacent side in a right triangle. Tangent of an angle equals the opposite side divided by the adjacent side.
Set Up Equation: Set up the equation using the tangent of $73$ degrees equals $30$ feet divided by the distance from you (let's call this distance $x$ ). $\newline$ $\tan(73) = \frac{30}{x}$
Solve for x: Solve for x by multiplying both sides by $x$ and then dividing both sides by $\tan(73)$ .
$x \cdot \tan(73) = 30$
$x = \frac{30}{\tan(73)}$
Calculate Value: Calculate the value of $\tan(73)$ using a calculator and then divide $30$ by this value. $\newline$ $x = \frac{30}{\tan(73)}$ $\newline$ $x \approx \frac{30}{3.2709}$ $\newline$ $x \approx 9.17 \text{ feet}$

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