A plane passes directly over you head at an altitude of 500 feet. Two seconds later you observe that is angle of elevation is 42 degrees. How far did the plane travel in 2 seconds?
Call that distance X.
Draw yourself a triangle. Call point O your position. Draw a vertical line up from there with height 500. From the top of that line, draw a horizontal flight path with length X. Draw the connecting hypotenuse. The angle the hypotenuse makes with the ground (which is parallel to the flight path) is 42 degrees. The tangent of that angle is X/500 = tan 42
Solve for X
450.202 feet
damn try finding the plane, check benghazi lmao
To answer this question, we can use trigonometry and basic geometry principles. Let me explain how you can find the distance traveled by the plane in 2 seconds.
First, let's draw a diagram to visualize the situation. We have a person on the ground, standing directly beneath a plane that is flying at an altitude of 500 feet. Two seconds later, the person observes the angle of elevation between the ground and the plane to be 42 degrees.
Now, we can break down the problem into two parts:
1. Triangular Relationship:
We have a right triangle formed by the ground, the person's line of sight, and the height of the plane. The angle of elevation is the angle formed between the person's line of sight and the horizontal ground. Since it is a right triangle, we can use trigonometric ratios to find the lengths of its sides.
In this case, we know that the opposite side of the triangle is the altitude of the plane, which is 500 feet. Let's call this side "opposite" (O). The adjacent side is the distance traveled by the plane in 2 seconds, which we're trying to find. Let's call this side "adjacent" (A). Finally, the hypotenuse of the triangle is the line of sight from the person to the plane.
2. Trigonometric Ratio:
We can use the tangent ratio (tan) to relate the angle of elevation and the sides of the triangle. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, we have:
tan(42 degrees) = O / A
Rearranging this equation, we can solve for A (the distance traveled by the plane in 2 seconds):
A = O / tan(42 degrees)
Substitute the known values:
A = 500 feet / tan(42 degrees)
Now, let's calculate the value.
Using a calculator, we find that the tangent of 42 degrees is approximately 0.9.
A ≈ 500 feet / 0.9 ≈ 555.55 feet
Therefore, the plane traveled approximately 555.55 feet in 2 seconds.