Question 1190090: Lara flies a helicopter over the well and drops a rope to measure her height above it. Exactly 125 m of rope is all she needs to touch the well; however, a steady wind is blowing the rope so it makes a straight line at an angle to the ground.
Meanwhile, back at the catapult, Harrison uses a rangefinder to determine that the helicopter is exactly 280 m away from the catapult, at an elevation of 15°.
Harrison radios Lara and confirms that the well, the helicopter and the catapult are all in the same vertical plane. Without making any further measurements, he now has enough information to set the distance for the catapult.
Harrison has one critical piece of information that you do not. Without it, you cannot determine the distance to the well with certainty. The information is not a measurement—Harrison will have no trouble determining it.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! The critical piece of information Harrison has (and you don't) is the **angle of the rope**.
Here's why:
1. **Lara's Information:** Lara knows the length of the rope (125m). However, because the wind is blowing the rope at an angle, this is the *hypotenuse* of a right triangle. She *cannot* determine her vertical height above the well without knowing the angle of the rope.
2. **Harrison's Information:** Harrison knows the *straight-line distance* (280m) and *elevation angle* (15°) from the catapult to the helicopter. This allows him to calculate the *vertical height* of the helicopter above the ground.
3. **The Missing Link:** To connect Lara's information to Harrison's, you need to know the angle of the rope. This would allow Lara to calculate the vertical distance from the helicopter *down* to the well. Since Harrison has already figured out the helicopters height from the ground, the difference will give the distance from the catapult to the well.
**How Harrison Solves It:**
1. **Harrison calculates helicopter's height:** Using trigonometry (specifically the sine function), Harrison can find the helicopter's vertical height (h) above the ground: h = 280 * sin(15°).
2. **Lara calculates vertical distance to well:** With the rope's angle (let's call it 'θ'), Lara can calculate the vertical distance (v) from the helicopter to the well: v = 125 * cos(θ).
3. **Harrison calculates distance to well:** The vertical distance from the ground to the well is h - v. With this vertical distance and the horizontal distance from the catapult to the point directly below the helicopter (280cos15), Harrison can use the Pythagorean theorem to calculate the straight line distance from the catapult to the well.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Not a math problem.
More like puzzle or gum that is chewed in the mouth for a long time.
I do not understand, why and for what reason it was submitted to this forum.
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