Kevin is flying an airplane at an altitude of 5300 feet.He sees his house on the ground at 45 degree angle of depression.What is kevin's horizontal distance from his house at this point?
Since the angle is 45° , the triangle is an isosceles right-angled triangle.
no work needed, the distance = 5300 ft
To find Kevin's horizontal distance from his house, we'll need to use trigonometry, specifically tangent.
First, let's draw a diagram to visualize the situation. We have Kevin flying at an altitude of 5300 feet and seeing his house on the ground at a 45-degree angle of depression. The distance we want to find is the horizontal distance from Kevin's current position to his house. Let's label this distance as "x".
Now, let's apply the tangent function to the given angle of depression (45 degrees) to find the ratio of the opposite side (which is the horizontal distance x) to the adjacent side (which is the altitude 5300 feet) in a right triangle. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
So we have: tan(45°) = x / 5300
To find x, we can rearrange the equation as follows:
x = 5300 * tan(45°)
Now, let's calculate the value of x using a calculator:
x ≈ 5300 * 1 ≈ 5300 feet
Therefore, Kevin's horizontal distance from his house is approximately 5300 feet.