Answer:
309.2 ft
Explanation:
We can represent the situation with the following figure
So to find the height from the car to the plane, we need to find the values of x and y using the formed triangles.
To find the value of x, we will use the trigonometric function tangent as follows
[tex]\tan 52=\frac{x}{150}[/tex]
Because x is the opposite side of the angle of 52 degrees and 150 is the adjacent side.
Then, solving for x, we get:
[tex]\begin{gathered} x=150\cdot\tan 52 \\ x=150\cdot1.28 \\ x=192\text{ ft} \end{gathered}[/tex]
In the same way, we can calculate the value of y as follows
[tex]\begin{gathered} \tan 38=\frac{y}{150} \\ y=150\cdot\tan 38 \\ y=150\cdot0.78 \\ y=117.2\text{ ft} \end{gathered}[/tex]
Therefore, the answer is
x + y = 192 ft + 117.2 ft = 309.2 ft
So, the plane is 309.2 ft above the car.
