Question

The air traffic control tower in Dublin, Ireland is 87.7 meters tall. If someone in the tower (assume they are at the top even though they would actually be slightly lower) measures the angle of inclination to a plane to be 17.4 degrees and the pilot communicates that the plane is currently flying at an altitude of 715 meters, how far away from the tower is the plane?see picture for a drawing of the scenario a classmate drew to help me visualize. any help appreciated!

Answer 1

the plane is 2097.99m away from the tower

Step-by-step explanation:

We need an illustration to solve this question:

From the diagram, CB is the distance from the tower to the plane

CF = tower's height

BF = plane's height

`\begin{gathered} To\text{ get CB, we will apply sine ratio} \\ \sin \text{ 17.4}\degree=\text{ }(opposite)/(hypotenuse) \\ \sin \text{ 17.4}\degree\text{ = }(AC)/(CB) \end{gathered}`
`\begin{gathered} \sin ce\text{ BF = AC + CF} \\ \text{and BF = 715m, CF = 87.7} \\ AC\text{ = BF - CF = 715 - 87.7} \\ AC\text{ = 627.3 m} \end{gathered}`
`\begin{gathered} \sin \text{ 17.4}\degree\text{ = }(627.3)/(CB) \\ CB\text{ (sin 17.4}\degree)\text{ = 627.3} \\ CB\text{ = }\frac{627.3}{\sin \text{ 17.4}\degree}\text{ = }(627.3)/(0.2990) \\ CB\text{ = }2097.99 \end{gathered}`

Hence, the plane is 2097.99m away from the tower