From the top of a cliff 200m high, and the angle of depression of a boat at sea is 35 degree. Find the distance between the boat and the foot of the cliff
did you draw a sketch? If so, it should b clear that
200/x = tan35°
now find x
just explain
To find the distance between the boat and the foot of the cliff, we can use trigonometric ratios, specifically the tangent function.
Let's define the given information:
- Height of the cliff (opposite side): 200m
- Angle of depression (angle between the line of sight from the top of the cliff to the boat and the horizontal): 35 degrees
Now, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side, to find the distance between the boat and the foot of the cliff.
Tangent theta (tan θ) = opposite side / adjacent side
In this case, the opposite side is the height of the cliff (200m), and the adjacent side is the distance between the boat and the foot of the cliff, which we need to find.
Using the formula for tangent:
tan θ = opposite side / adjacent side
Plugging in the values:
tan 35° = 200 / adjacent side
Now, let's solve for the adjacent side:
adjacent side = opposite side / tan θ
adjacent side = 200 / tan 35°
Using a calculator, we can evaluate this expression to find the adjacent side:
adjacent side ≈ 200 / 0.7002 ≈ 285.626
Therefore, the distance between the boat and the foot of the cliff is approximately 285.626 meters.
To find the distance between the boat and the foot of the cliff, we can use trigonometry. Specifically, we can use the tangent function.
Let's denote the distance between the boat and the foot of the cliff as x.
Since the angle of depression is given as 35 degrees, we can write:
tan(35) = opposite/adjacent
In this case, the opposite side is 200m (the height of the cliff) and the adjacent side is x (the distance between the boat and the foot of the cliff).
Therefore, we can write:
tan(35) = 200/x
To find x, we can rearrange the equation:
x = 200 / tan(35)
Using a calculator, we can evaluate the tangent of 35 degrees:
tan(35) ≈ 0.7002
Now, we can substitute this value into the equation to find x:
x = 200 / 0.7002
x ≈ 285.69
Therefore, the distance between the boat and the foot of the cliff is approximately 285.69 meters.