A plane takes off from the ground at a 14-degree angle. After flying straight for 10,000 feet, what is the altitude of the plane?
x/10000 = sin 14°
x/10000=sin(14º)
x=10000sin(14º) , since sin(14º)=0.24192
x=10000*(0.24192)
x=2419.2 feet
q2111
To find the altitude of the plane, we can use trigonometry.
First, we need to understand the given information. We know that the plane takes off from the ground at a 14-degree angle. This angle is measured with respect to the horizontal ground.
Next, we need to identify the right triangle formed by the plane's altitude, the ground, and the straight distance the plane has flown.
The opposite side of the triangle represents the altitude of the plane, which is the value we want to find. The adjacent side represents the straight distance the plane has flown, which is given as 10,000 feet. The angle between these two sides is 14 degrees.
Now, we can use the trigonometric function tangent (tan) to find the altitude of the plane. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, we can use the formula:
tan(angle) = opposite / adjacent
Plugging in the values we have:
tan(14 degrees) = altitude / 10,000 feet
Now, we can solve for the altitude by multiplying both sides of the equation by 10,000 feet:
altitude = tan(14 degrees) * 10,000 feet
To get the actual numerical answer, you can use a scientific calculator or an online calculator to find the tangent of 14 degrees. Plugging in the values:
altitude ≈ 2437.75 feet
Therefore, the altitude of the plane after flying straight for 10,000 feet is approximately 2437.75 feet.