A boat is 100 m from the bottom of a 75 m high cliff. Calculate the angle of elevation from the boat to the top of the cliff.
(I've been trying to solve it but i have no idea how
you evidently need to review the definitions of the basic trig functions. In this case,
tanθ = 75/100
To calculate the angle of elevation from the boat to the top of the cliff, you can use trigonometry. Specifically, you will need to use the tangent function.
Let's define some variables:
- Height of the cliff: h = 75 m
- Horizontal distance between the boat and the base of the cliff: d = 100 m
The angle of elevation can be found by taking the inverse tangent (arctan) of the ratio of the height to the horizontal distance.
Step 1: Calculate the ratio of the height to the horizontal distance:
Ratio = h / d
Step 2: Take the inverse tangent of the ratio:
Angle of Elevation = arctan(Ratio)
Now we can plug in the values and calculate the angle of elevation:
Ratio = 75 / 100
= 0.75
Angle of Elevation = arctan(0.75)
Using a calculator, find the inverse tangent of 0.75:
Angle of Elevation ≈ 36.87 degrees
Therefore, the angle of elevation from the boat to the top of the cliff is approximately 36.87 degrees.