A helicopter pilot sights a landmark at an angle of depression of 22°. The altitude of the helicopter is 1450 feet. To the nearest foot, what is the horizontal distance from the helicopter to the landmark?

3589

Use the tangent function. I will be happy to critique your work.

IS IT tan22=x\1450

1450tan22

Well, I hope that helicopter pilot doesn't get too distracted by the beautiful scenery below!

Anyway, let's crunch some numbers. We have an angle of depression of 22° and an altitude of 1450 feet. We can use a bit of trigonometry to find the horizontal distance:

tan(θ) = opposite/adjacent

In this case, the opposite side is the altitude of the helicopter (1450 feet) and the hypotenuse is the horizontal distance we're trying to find. So, let's rearrange the equation:

tan(22°) = 1450 ft/horizontal distance

To solve for the horizontal distance, we can multiply both sides by the horizontal distance:

horizontal distance = 1450 ft / tan(22°)

Now, let's calculate it:

horizontal distance = 1450 ft / tan(22°)

horizontal distance ≈ 3504 feet

So, to the nearest foot, the horizontal distance from the helicopter to the landmark is 3504 feet. I hope that helps, and keep those helicopters flying high!

To find the horizontal distance from the helicopter to the landmark, we can use trigonometry.

Let's start by drawing a diagram to visualize the problem. In the diagram, the helicopter is at point A, and the landmark is at point B. The angle of depression is the angle formed between the horizontal line (from the helicopter to the landmark) and the line of sight from the helicopter to the landmark.

Now, we can label some of the given information. The angle of depression is 22°, and the altitude of the helicopter is 1450 feet. Let's label the altitude as 'h' and the horizontal distance as 'x'.

According to trigonometry, we know that tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the tangent of the angle of depression is equal to the altitude divided by the horizontal distance.

So, we can write the equation as follows:

tan(22°) = h / x

Substituting the given values, we have:

tan(22°) = 1450 / x

Now, let's solve for x. We can rearrange the equation as follows:

x = 1450 / tan(22°)

Using a calculator, we can find the value of tan(22°) to be approximately 0.40403.

Now, plugging in the values, we have:

x = 1450 / 0.40403

Calculating this value, we get:

x ≈ 3589.401

Therefore, the horizontal distance from the helicopter to the landmark is approximately 3589.401 feet. Rounded to the nearest foot, the answer is 3589 feet.