The distance of a boat from a bridge 120 m high above sea level is 200m. Calculate the angle of elevation of the bridge from the boat.
Tan A = 120/200
A =
To calculate the angle of elevation of the bridge from the boat, we can use trigonometry. The angle of elevation is the angle between the horizontal line (sea level) and the line of sight from the boat to the top of the bridge.
We have a right triangle where the height of the bridge (opposite side) is given as 120 m and the horizontal distance from the boat to the bridge (adjacent side) is given as 200 m.
Using the tangent function, we can calculate the angle of elevation as follows:
tan(θ) = opposite/adjacent
tan(θ) = 120/200
Now we can solve for θ (the angle of elevation):
θ = tan^(-1) (120/200)
To find this angle using a calculator, follow these steps:
1. Divide 120 by 200, and calculate the ratio. In this case, the ratio is 0.6.
2. Take the inverse tangent (tan^(-1)) of 0.6. The result is the angle in radians.
3. If you want the angle in degrees, convert the radians to degrees by multiplying by 180/π (approximately 57.3 degrees).
So, using a calculator, we have:
θ ≈ tan^(-1) (0.6) ≈ 30.96 degrees
Therefore, the angle of elevation of the bridge from the boat is approximately 30.96 degrees.