A plane takes off on a runway that is horizontally 915 ft from a building, 121 ft high. What is the minimum angle of elevation of its take off to assure of going over the building if it flies in a straight line?
To find the minimum angle of elevation needed for the plane to clear the building, we can use the tangent function.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the building (121 ft), and the adjacent side is the horizontal distance between the plane and the building (915 ft).
So, we have:
tangent(angle) = opposite / adjacent
tangent(angle) = 121 ft / 915 ft
To find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(121 ft / 915 ft)
Using a calculator or trigonometric table, we find that the angle is approximately 7.5 degrees.
Therefore, the minimum angle of elevation the plane needs to take off to clear the building is approximately 7.5 degrees.
To find the minimum angle of elevation required for the plane to clear the building, we can use trigonometry.
Step 1: Draw a diagram representing the situation. Label the horizontal distance from the building to the plane's starting point as 915 ft and the height of the building as 121 ft.
Step 2: Let the angle of elevation be represented by θ. We want to find the minimum value of θ that ensures the plane flies over the building.
Step 3: We can use the tangent function (tan) to solve this problem. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the building (121 ft) and the adjacent side is the horizontal distance from the building to the plane's starting point (915 ft). Therefore, we have the equation:
tan(θ) = opposite/adjacent = 121/915
Step 4: Now, solve for θ. Take the inverse tangent (arctan) of both sides of the equation to isolate θ:
θ = arctan(121/915)
Step 5: Use a calculator to evaluate the arctan(121/915) to find the angle in radians.
Step 6: Convert the angle from radians to degrees (if necessary) by multiplying it by 180/π (180 divided by the value of π, which is approximately 3.14159). This will give you the angle in degrees.
The resulting value is the minimum angle of elevation in degrees that the plane must have to clear the building if it flies in a straight line.