the angle of depression of a boat from the top of a cliff is 58.if the cliff is 10.5m high how far is the boat from the foot of the cliff
guessing degrees ...
distance = 10.5 m / tan(58º)
Well, I guess the boat must have been feeling a bit down with that angle of depression! But don't worry, I'll do my best to help you out.
To find the distance from the boat to the foot of the cliff, we can use a little bit of trigonometry. Since we have the angle of depression, we can use the tangent function.
Tangent(theta) = Opposite / Adjacent
In this case, the opposite side is the height of the cliff (10.5m) and the adjacent side is the distance we're looking for.
Tangent(58) = 10.5m / Distance
To solve for the distance, we rearrange the equation:
Distance = 10.5m / Tangent(58)
Using a calculator, we find that the tangent of 58 degrees is approximately 1.61.
Distance = 10.5m / 1.61 ≈ 6.52m
So, according to my calculations, the boat is approximately 6.52 meters away from the foot of the cliff.
To find the distance between the boat and the foot of the cliff, we can use the tangent function, as the angle of depression is given and the height of the cliff is known.
Let's denote the distance between the boat and the foot of the cliff as "d".
We can set up the following equation using the tangent function:
tan(angle) = opposite/adjacent
In this case, the angle is 58 degrees and the opposite side length is 10.5m (height of the cliff). We want to find the adjacent side length, which is the distance between the boat and the foot of the cliff (d).
tan(58) = 10.5 / d
To solve for d, we can rearrange the equation:
d = 10.5 / tan(58)
Using a calculator, we find:
d ≈ 7.61m
Therefore, the boat is approximately 7.61m away from the foot of the cliff.
To find the distance between the boat and the foot of the cliff, we can use basic trigonometry and the concept of angle of depression.
Let's label the distance we want to find as "x".
From the information given, we know that the angle of depression is 58 degrees and the height of the cliff is 10.5 meters.
In this scenario, we have a right triangle formed by the cliff, the boat, and the horizontal ground. The angle of depression is the angle between the horizontal ground and the line of sight to the boat.
We can use the trigonometric function "tangent" to relate the angle of depression and the sides of the right triangle:
tangent(angle of depression) = opposite side / adjacent side
In this case, the opposite side is the height of the cliff (10.5m) and the adjacent side is the distance we want to find (x).
So, we have the equation:
tan(58 degrees) = 10.5m / x
To solve for x, we can rearrange the equation:
x = 10.5m / tan(58 degrees)
Now, we can plug in the values and calculate the distance:
x = 10.5m / tan(58 degrees)
Using a calculator, we find:
x ≈ 10.5m / 1.6643
x ≈ 6.305m
Therefore, the boat is approximately 6.305 meters away from the foot of the cliff.