An observer (0) spots a plane flying at a 55 degree angle to his horizontal line of sight.If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (0)
21/x = sin 55°
To find the distance (x) from the plane (P) to the observer (0), we can use trigonometry.
Let's draw a diagram to visualize the scenario. The observer (0) is on the ground, and the plane (P) is flying at a 55-degree angle to the observer's horizontal line of sight. Let's consider the altitude (h) of the plane, which is given as 21,000 ft.
P
/
/
x /
/ 55°
/
/
O
In this right-angled triangle, the side opposite to the angle of 55 degrees is the altitude of the plane (h), and the desired side adjacent to the angle is the distance (x) from the plane to the observer.
We can use the trigonometric function "tan" to relate the angle and the sides of the triangle:
tan(angle) = opposite/adjacent
In this case, tan(55 degrees) = h/x
Now, let's substitute the given value of the altitude:
tan(55 degrees) = 21,000/x
We need to isolate x, so let's solve for it.
Rearranging the equation, we have:
x = 21,000 / tan(55 degrees)
Using a scientific calculator or an online trigonometric calculator, we can calculate the value of tan(55 degrees). Let's assume it is approximately 1.428.
Substituting this value in the equation, we get:
x = 21,000 / 1.428
Now, we can solve for x:
x = 14,706.29 ft
Therefore, the distance from the plane to the observer is approximately 14,706.29 ft.