Katie is watching a helicopter flying at an altitude of 5 miles. If the angle of elevation is pi/3 , the distance between Katie and the helicopter is approximately miles.
NextReset
draw a diagram. You can see that
5/x = sin π/3
To find the distance between Katie and the helicopter, we can use trigonometry and the angle of elevation. The angle of elevation, in this case, is π/3, which means it forms a right triangle with the altitude of 5 miles.
In a right triangle, the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the tangent of the angle is equal to the altitude divided by the distance between Katie and the helicopter.
So, let's set up the equation:
tan(π/3) = 5 / x
To find x, we can multiply both sides of the equation by x:
x * tan(π/3) = 5
Now, we can solve for x by dividing both sides of the equation by tan(π/3):
x = 5 / tan(π/3)
Using a calculator, we find:
x ≈ 8.66 miles
Therefore, the distance between Katie and the helicopter is approximately 8.66 miles.
To find the distance between Katie and the helicopter, we can use trigonometry. Specifically, we can use the tangent function.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the altitude of the helicopter (5 miles) and the adjacent side is the distance between Katie and the helicopter (which we want to find).
Let's call the distance between Katie and the helicopter "d". The tangent of the angle of elevation is given by the formula:
tan(angle) = opposite/adjacent
In this case, we can write the equation as:
tan(pi/3) = 5/d
To solve for "d", we can rearrange the equation:
d = 5 / tan(pi/3)
Now, let's calculate the value of tan(pi/3):
tan(pi/3) ≈ 1.73205
Substituting this value into the equation:
d ≈ 5 / 1.73205 ≈ 2.8875
Therefore, the distance between Katie and the helicopter is approximately 2.8875 miles.