Math Problem Statement

a kite flying a height of 70m is attached to a string inclinedat 44° to the horizontal.What is the length of the string?

Solution

To determine the length of the string, we can use trigonometry. Specifically, the sine function is appropriate here because it relates the angle of inclination, the height (opposite side), and the length of the string (hypotenuse).

Given:

  • Height of the kite (hh) = 70 meters
  • Angle of inclination (θ\theta) = 44°

We need to find the length of the string (LL).

The sine of the angle is given by: sin(θ)=oppositehypotenuse=hL\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L}

Rearranging to solve for LL: L=hsin(θ)L = \frac{h}{\sin(\theta)}

Substituting the known values: L=70sin(44)L = \frac{70}{\sin(44^\circ)}

Now, let's calculate the value of LL.

L700.6947100.8 metersL \approx \frac{70}{0.6947} \approx 100.8 \text{ meters}

So, the length of the string is approximately 100.8 meters.

Would you like further details or have any questions about this calculation?


Here are five related questions:

  1. What if the angle of inclination was 60°? How would the string length change?
  2. How would the length change if the kite was flying at a height of 100 meters with the same angle?
  3. What is the relationship between the angle of inclination and the length of the string?
  4. Can we calculate the horizontal distance from the point where the string is tied to the ground to the point directly below the kite?
  5. What would be the length of the string if the kite's height was doubled, keeping the angle the same?

Tip: Remember that in right-angled triangles, the sine function is very useful for relating angles to the ratio of the opposite side over the hypotenuse.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Trigonometry
Right triangle trigonometry

Formulas

Sine function: sin(θ) = opposite / hypotenuse

Theorems

-

Suitable Grade Level

High School