Question

2. Juan is flying a piscucha. He is releasing the thread, having his hand at the height of the throat, which is 1.68 meters from the ground, if the thread forms an angle of elevation of 50°, at what height is the piscucha at the moment that Juan has released 58 meters of the thread?

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Dexter

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STEP BY STEP SOLUTION:
Let's denote:
- h as the height of the piscucha above the ground at a given moment,
- d as the distance between Juan's hand and the point directly below the piscucha (which is 58 meters since he has released 58 meters of the thread),
- a as the angle of elevation (50° in this case).
The relationship between the height h, the distance d, and the angle of elevation a can be represented by the sin function:
\[ \sin(a) = \frac{h}{d} \]
In this scenario:
\[ \sin(50°) = \frac{h}{58 \, \text{m}} \]
Now, solve for h:
\[ h = 58 \, \text{m} \times \sin(50°) \]
Using a calculator:
\[ h = 44.43 \, \text{meters} \]
ANSWER:
Therefore, at the moment Juan has released 58 meters of the thread, the piscucha is \( 44.43 \, \text{meters} + 1.68 \, \text{meters} = 46.11 \, \text{meters} \) above the ground.

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