Kite Height Calculation Using Trigonometry

To find the height of the kite from the ground, we need to consider the length of the thread, the angle of elevation, and the height of the person.

The problem involves a right-angled triangle formed by the kite thread, the horizontal distance from the observer, and the vertical height of the kite above the observer's hand.

Steps to Find Kite Height

• Identify Given Values:

  • Length of the thread (hypotenuse, $h_{thread}$) = 296 m
  • Angle of elevation ($\theta$) = 30°
  • Height of the person ($h_{person}$) = 2 m

• Calculate Height Above Hand:

  Use the sine function to find the height of the kite above the person's hand ($h_{above\_person}$). The sine of the angle is the ratio of the opposite side (height above hand) to the hypotenuse (thread length).

  $ \sin(\theta) = \frac{h_{above\_person}}{h_{thread}} $

  Rearranging the formula:

  $ h_{above\_person} = h_{thread} \times \sin(\theta) $

  Substitute the values:

  $ h_{above\_person} = 296 \, \text{m} \times \sin(30^\circ) $

  Since $\sin(30^\circ) = 0.5$:

  $ h_{above\_person} = 296 \, \text{m} \times 0.5 = 148 \, \text{m} $

• Calculate Total Height from Ground:

  Add the height of the person to the height calculated above the hand to get the total height of the kite from the ground ($H_{kite}$).

  $ H_{kite} = h_{above\_person} + h_{person} $

  $ H_{kite} = 148 \, \text{m} + 2 \, \text{m} = 150 \, \text{m} $

Final Answer

The height of the kite from the ground is 150 m.