a boat is approaching a cliff known to be 50m tall. if the angle of elevation from the boat is 60 degrees, how far away is the boat from the cliff?
To find the distance between the boat and the cliff, we can use trigonometry. Let x represent the distance between the boat and the cliff.
In a right triangle, the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the angle of elevation is 60 degrees, the opposite side is 50 m (height of the cliff), and the adjacent side is x (distance between the boat and the cliff).
So, we can write the equation as:
tan(60°) = opposite/adjacent
tan(60°) = 50/x
Using a scientific calculator, we can find the tangent of 60 degrees to be √3. Therefore, the equation becomes:
√3 = 50/x
To solve for x, we can multiply both sides of the equation by x:
√3 * x = 50
x = 50/√3
To simplify the expression, we can rationalize the denominator by multiplying both the numerator and denominator by √3:
x = (50/√3) * (√3/√3)
x = 50√3/3
Therefore, the boat is approximately 28.87 m away from the cliff.