Question

NO LINKS!!! URGENT HELP PLEASE!!!!

At the Detroit Metro there is a cell tower located near the end of the runway. In order for the plane to clear the tower safely it must take off at an angle of no less than 25 degrees. If the tower is 200 feet tall, how far away should the plane take off in order to safely avoid the tower?

Answer 1

Explanation:

To solve the problem, we can use trigonometry. Let's call the distance the plane needs to be from the base of the tower "x". We can then use the tangent function to find the height of the tower that the plane needs to clear:

tan(25) = 200/x

To solve for x, we can cross-multiply:

x * tan(25) = 200

Then, we can divide both sides by tan(25):

x = 200 / tan(25)

Using a calculator, we get:

x ≈ 437.4 feet

Therefore, the plane needs to take off at a distance of at least 437.4 feet from the base of the tower in order to safely avoid it.

Answer 2

The plane should take off 428.9 feet from the base of the tower (to the nearest tenth).

Explanation:

The given scenario can be modelled as a right triangle, where the length of the runway is the base of the triangle and the height of the tower is the height of the triangle.

Given the take-off angle is 25° and the tower is 200 feet tall, we can use the tangent trigonometric ratio to find the horizontal distance from the base of the tower that the plane should take off in order to safely avoid the tower.

`\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=(O)/(A)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}`

Given:

• θ = 25°
• O = 200 ft
• A = x

Substitute the values into the ratio and solve for x:

`\implies \tan 25^(\circ)=(200)/(x)`

`\implies x=(200)/(\tan 25^(\circ))`

`\implies x=428.90138...`

`\implies x=428.9\; \sf ft\;(nearest\;tenth)`

Therefore, the plane should take off 428.9 feet from the base of the tower (to the nearest tenth).