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.
Draw a right triangle figure.
Altitude (the vertical side) = 100
40 degrees = angle of hypotentuse above horizontal.
(Ground Distance)*tan 40 = 100
Ground distance = 100/tan 40 = 119.2 ft
I used a pocket calculator instead of a trig chart. You could also search tan (40 degrees) on Google.
http://www.google.com/search?hl=en&rlz=1G1GGLQ_ENUS366&ie=ISO-8859-1&q=tan%2840+degrees%29&btnG=Search
A 20 ft. beam leans against a wall. The beam reaches the wall 13.9 ft. above the ground. What is the measure of the angle formed by the beam and the ground?
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Why did the plane join a comedy club? Because it wanted to improve its altitude! But don't worry, I've got your question covered (no pun intended!).
To find out how much ground distance the plane has covered, we'll use some trigonometry. We know that the altitude is 100 feet and the angle of ascent is 40°. So, we can use the sine function to find the ground distance.
The formula we'll use is:
Ground Distance = Altitude / sin(Angle)
Plugging in the values:
Ground Distance = 100 / sin(40°)
Using a trigonometric chart or calculator, we find that sin(40°) is approximately 0.6428 (rounded to four decimal places).
So, Ground Distance = 100 / 0.6428 ≈ 155.3 feet.
Therefore, the plane has covered approximately 155.3 feet of ground distance. Keep reaching for the skies!
To solve this problem, we can use trigonometry to find the ground distance covered by the plane.
First, we need to understand that the angle of 40° is between the hypotenuse (the distance traveled by the plane) and the vertical side (the altitude reached by the plane, which is 100 feet). We need to find the length of the base side, which represents the ground distance covered.
Using the trigonometric chart, we find that the trigonometric function for finding the length of the base side (adjacent side) is the cosine function (cos). The formula for finding the adjacent side is:
adjacent side = hypotenuse × cos(angle)
In this case, the adjacent side is the ground distance and the hypotenuse is the distance traveled by the plane, which we need to find.
We can substitute the known values into the formula:
adjacent side = 100 feet × cos(40°)
Using a calculator, we find that the cosine of 40° is approximately 0.766.
So, the ground distance covered by the plane is:
ground distance = 100 feet × 0.766
Calculating this, we find that the ground distance is approximately 76.6 feet.
Therefore, the plane has covered approximately 76.6 feet of ground distance when it reaches an altitude of 100 feet, ascending at a 40° angle.