A plane ascends at a 40° angle. When it reaches an altitude of one hundred feet, how much ground distance has it covered? To solve, use the trigonometric chart. Round the answer to the nearest tenth.
height/distance= tan40
distance= height/tangent(40)
To solve this problem, we can use trigonometry and the given angle to find the ground distance covered by the plane.
First, let's draw a diagram to help visualize the problem. Assume the plane starts at point A on the ground, and point B represents the final position of the plane at an altitude of 100 feet. The angle of ascent is 40 degrees.
Now, we know that the opposite side of the triangle formed by the plane's ascent is the altitude of 100 feet, and we need to find the length of the adjacent side, which represents the ground distance covered.
In trigonometry, we use the tangent function to relate the opposite and adjacent sides of a right triangle. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.
Referring to a trigonometric chart or calculator, we find that the tangent of 40 degrees is approximately 0.8391. Let's use this value to calculate the ground distance covered.
We can set up the following equation using the tangent function:
tangent(angle) = opposite / adjacent
tangent(40 degrees) = 100 feet / adjacent
0.8391 = 100 / adjacent
To isolate the adjacent side, we can rearrange the equation:
adjacent = 100 feet / 0.8391
adjacent ≈ 119.32 feet
Therefore, the plane has covered approximately 119.32 feet of ground distance when it reaches an altitude of 100 feet.
Rounding this answer to the nearest tenth, we get the final result:
The plane has covered approximately 119.3 feet of ground distance.