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.
Assuming a uniform ascending angle of 40° and an altitude of 100', the ground distance is given by
tan(40°) = altitude / ground distance
By the way, tan(40°) = 0.8391
Can you take it from here?
Do you have a trigonometric chart, or are you using the four-figure tables?
Is it, 0.008391
To solve this problem, we can use trigonometry. The given information states that the plane ascends at a 40° angle and reaches an altitude of one hundred feet. We need to find out how much ground distance it has covered.
Let's break down the problem into two parts: the altitude and the ground distance.
1. Altitude: The altitude of the plane is given as one hundred feet. This represents the opposite side of the right triangle formed by the plane's ascent. In trigonometry, the opposite side of an angle is typically represented as the side "a" in the formula. Therefore, we have a = 100 feet.
2. Angle: The angle of ascent is given as 40°. This is the angle between the hypotenuse (plane's path) and the ground. In trigonometry, this side is typically represented as the hypotenuse "h" in the formula. Therefore, we have h = ?
Now, using trigonometry, we can relate the opposite side (a), hypotenuse (h), and angle (θ) using the sine function:
sin(θ) = a / h
Rearranging the formula, we can solve for h:
h = a / sin(θ)
Plugging in the values from the problem, we have:
h = 100 / sin(40°)
To find the answer, we can refer to a trigonometric chart or use a scientific calculator. The sine of 40° is approximately 0.6428.
Therefore:
h = 100 / 0.6428
h ≈ 155.55 feet
So, the plane has covered approximately 155.55 feet of ground distance when it reaches an altitude of one hundred feet.