from the top of a bridge over the burlington canal, maria looks down at a sailboat at an angle of depression 15 degrees.the bridge is 18m above the water. calculate the horizontal distance from the bridge to the sailboat

You are looking at a right triangle of which one angle is 15°, the opposite side is 18m (vertical).

From the definition of tangent,
tan(θ)=opposite (18m) / adjacent (H)
where H is the horizontal distance required.
Solve for H since θ and opposite are known.

hii

To calculate the horizontal distance from the bridge to the sailboat, we can use the tangent function.

Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the angle of depression is given as 15 degrees and the opposite side is the height of the bridge, which is 18 meters.

Using the formula for tangent:
tan(angle) = opposite/adjacent

Plugging in the values:
tan(15 degrees) = 18/adjacent

We want to find the adjacent side, so rearranging the equation:
adjacent = 18 / tan(15 degrees)

Using a scientific calculator:
adjacent = 18 / tan(15)

Calculating this, the horizontal distance from the bridge to the sailboat is approximately 68.23 meters.

To calculate the horizontal distance from the bridge to the sailboat, you can use trigonometry.

Let's consider the geometry of the situation. The bridge, the sailboat, and the line of sight from Maria's viewpoint form a right triangle.

The angle of depression is the angle between the line of sight (from Maria's eye level) and the horizontal line. In this case, the angle of depression is 15 degrees.

The height of the bridge above the water is given as 18m.

We can use the tangent function, which relates the opposite side to the adjacent side of a right triangle:

tangent(angle) = opposite / adjacent

In this case, the adjacent side is the horizontal distance we want to find, and the opposite side is the height of the bridge.

So, the equation is:

tangent(15 degrees) = 18 / x

To find x, we need to isolate it on one side of the equation by multiplying both sides by x:

x * tangent(15 degrees) = 18

Finally, we can solve for x by dividing both sides by tangent(15 degrees):

x = 18 / tangent(15 degrees)

Calculating this using a scientific calculator, the horizontal distance is approximately 63.73 meters.

Therefore, the horizontal distance from the bridge to the sailboat is approximately 63.73 meters.