A ship is sighted from the top of a lighthouse. The angle of depression from the lighthouse to the top of the ship is 45 degrees. The distance from the top of the lighthouse directly to the ship is 4 miles. Calculate the horizontal distance of the ship from the bottom of the lighthouse. Put your answer to 2 decimal places
The hypotenuse is 4 and the angle is 45 degrees?
You can do it.
sin45 =x/4 x=sin45*4 x=2.83m
I think that is the height, not the distance, but it does not matter because with 45 degrees they are identical :)
To calculate the horizontal distance of the ship from the bottom of the lighthouse, we can use trigonometry, specifically the tangent function.
Let's denote the horizontal distance as 'x'. We can create a right triangle, where the angle of depression is 45 degrees and the distance from the top of the lighthouse to the ship is 4 miles. The side adjacent to the angle of depression is the horizontal distance 'x', and the side opposite the angle of depression is the distance of the ship from the lighthouse directly, which is 4 miles.
Now, we can use the tangent function:
tan(angle) = opposite / adjacent
Using the given values, we can substitute them into the equation:
tan(45 degrees) = 4 / x
Now, we can solve for 'x' by isolating it:
x = 4 / tan(45 degrees)
To calculate the value of 'x', we need to find the value of the tangent of 45 degrees. Using a scientific calculator or any trigonometric table, we can determine that the tangent of 45 degrees is 1.
Substituting this value back into the equation:
x = 4 / 1
x = 4 miles
Therefore, the horizontal distance of the ship from the bottom of the lighthouse is 4 miles.