Question

a man observes a balloon at a 64° angle of elevation. he knows the balloon is hovering directly above a point on the ground, 120 feet to the east, as shown in the figure below. sin 64°≈0.8988 cos 64°≈0.4384 tan 64°≈2.0503 if the man is 5 feet tall, what is h, the altitude of the balloon, to the nearest whole foot? use the trigonometric ratios provided and enter your answer in the box. feet

Explanation:

Step1: Determine the height from eye - level

The man's eye - level height above the ground is 5 feet. The vertical distance from the point 120 feet east of the man to the balloon (excluding the man's height) can be found using the tangent function.
Let the vertical distance from the 120 - foot point to the balloon (excluding the man's height) be $y$. We know that $\tan\theta=\frac{y}{x}$, where $\theta = 64^{\circ}$ and $x = 120$ feet.
Since $\tan64^{\circ}\approx2.0503$ and $x = 120$ feet, we have $y=x\tan\theta$.
$y = 120\times\tan64^{\circ}$.
$y=120\times2.0503 = 246.036$ feet.

Step2: Calculate the altitude of the balloon

The altitude $h$ of the balloon is the sum of the vertical distance from the 120 - foot point to the balloon and the man's height.
$h=y + 5$.
$h=246.036+5=251.036\approx251$ feet.

Answer:

251