A plane flies towards a ground-based radar dish. Radar locates the plane at a distance D = 41 km from the dish, at an angle θ = 52° above horizontal.
What is the plane’s horizontal distance, DH in meters, from the radar dish??
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Well, if the plane is flying towards the radar dish, we can say that it's really radar-ing the plane! But let's not get distracted by the puns.
To solve this problem, we need to break down the distance and angle information given. We can use trigonometry to find the horizontal distance (DH) of the plane from the radar dish.
In this case, we're given the hypotenuse of the triangle, which is the distance (D) of the plane from the radar dish. The angle (θ) provided is the angle above the horizontal.
Now let's use some trigonometry magic! We can use the sine function to find the opposite side of the triangle (DH) which represents the vertical distance:
sin(θ) = opposite side / hypotenuse
sin(52°) = DH / 41 km
Now we just need to solve for DH. To do that, we can rearrange the equation:
DH = sin(52°) * 41 km
Remember to convert km to meters by multiplying by 1000:
DH = sin(52°) * 41 km * 1000
So, the plane's horizontal distance (DH) from the radar dish is approximately DH = 32,898 meters.
I hope that clears things up for you! If you have any other questions, feel free to ask.
To find the plane's horizontal distance from the radar dish (DH), we can use trigonometry.
The given information includes the distance from the dish (D) and the angle above the horizontal (θ). We can use the tangent function to relate these values.
The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the distance above the horizontal (D sin(θ)), and the adjacent side is the horizontal distance (DH).
So, we have the equation: tan(θ) = (D sin(θ)) / DH
Now, we can rearrange the equation to solve for DH:
DH = (D sin(θ)) / tan(θ)
Substituting the given values into the equation:
D = 41 km = 41,000 meters
θ = 52°
Now we can calculate DH:
DH = (41,000 sin(52°)) / tan(52°)
Using a calculator, we can evaluate the trigonometric functions:
sin(52°) ≈ 0.788
tan(52°) ≈ 1.279
DH ≈ (41,000 * 0.788) / 1.279
DH ≈ 25,433 meters
Therefore, the plane's horizontal distance from the radar dish is approximately 25,433 meters.