An airplane takes off 200 yards in front of a 180 yard building. Find the angle of elevation for the plane so it does not hit the building.

Triangle Consideration: To find the angle of elevation, we need to consider the airplane's takeoff point and the height of the building as a right-angled triangle. The distance from the airplane's takeoff point to the building is the adjacent side of the triangle, and the height of the building is the opposite side. We can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle, to find the angle of elevation.Tangent Function Application: The tangent of the angle of elevation (θ) is equal to the height of the building (opposite side) divided by the distance from the takeoff point to the building (adjacent side). So, we have: tan(θ) = height of the building / distance from takeoff point tan(θ) = 180 yards / 200 yardsCalculation of tan(θ): Now we calculate the value of tan(θ): tan(θ) = 180 / 200 tan(θ) = 0.9Finding Angle θ: To find the angle θ, we need to take the arctangent (inverse tangent) of 0.9. We can use a calculator to do this. θ = arctan(0.9)Final Angle Calculation: Using a calculator, we find that: θ ≈ arctan(0.9) ≈ 42.01 degrees

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An airplane takes off 200 yards in front of a 180 yard building.
Find the angle of elevation for the plane so it does not hit the building.

An airplane takes off $200$ yards in front of a $180$ yard building. $\newline$ Find the angle of elevation for the plane so it does not hit the building.

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Q. An airplane takes off

200

yards in front of a

180

yard building.

\newline

Find the angle of elevation for the plane so it does not hit the building.

Triangle Consideration: To find the angle of elevation, we need to consider the airplane's takeoff point and the height of the building as a right-angled triangle. The distance from the airplane's takeoff point to the building is the adjacent side of the triangle, and the height of the building is the opposite side. We can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle, to find the angle of elevation.
Tangent Function Application: The tangent of the angle of elevation $\theta$ is equal to the height of the building (opposite side) divided by the distance from the takeoff point to the building (adjacent side). So, we have: $\newline$ $\tan(\theta) = \frac{\text{height of the building}}{\text{distance from takeoff point}}$ $\newline$ $\tan(\theta) = \frac{180 \text{ yards}}{200 \text{ yards}}$
Calculation of $\tan(\theta):$ Now we calculate the value of $\tan(\theta):$ $\tan(\theta) = \frac{180}{200}$ $\tan(\theta) = 0.9$
Finding Angle $\theta$ : To find the angle $\theta$ , we need to take the arctangent (inverse tangent) of $0.9$ . We can use a calculator to do this. $\newline$ $\theta = \text{arctan}(0.9)$
Final Angle Calculation: Using a calculator, we find that: $\theta \approx \arctan(0.9) \approx 42.01$ degrees