a boy is flying a kite from a string of length 150m. if the string is taut and makes an angle of 67 degrees with the horizontal,what is the height of the kite
sin(A)=opposite side/hypotenuse
sin(67)=h/150
h=150*sin(67)
To find the height of the kite, we can use the trigonometric function of sine.
The given information is as follows:
- Length of the string (hypotenuse): 150 m
- Angle with the horizontal: 67 degrees
Step 1: Identify the right triangle in the problem.
Here, the string of the kite forms the hypotenuse of the right triangle. The height of the kite is the opposite side, and the horizontal distance from the boy to the kite is the adjacent side.
Step 2: Identify the relevant trigonometric function.
Since we are looking for the height of the kite (opposite side), and we know the hypotenuse, we can use the sine function.
sin(θ) = opposite / hypotenuse
Step 3: Calculate the height of the kite.
Using the formula sin(67) = opposite / 150, rearrange the formula to solve for the opposite side (height):
height = sin(67) * 150
Using a calculator, compute the value:
height ≈ 138.5 m
Therefore, the height of the kite is approximately 138.5 meters.
To find the height of the kite, we can use trigonometry and the given information.
Let's consider a right-angled triangle formed by the height of the kite, the string of the kite, and the horizontal ground. The height of the kite represents the opposite side of the triangle, and the string of the kite represents the hypotenuse.
Using trigonometric ratios, we can use the sine function to find the height:
sin(θ) = opposite/hypotenuse
Given that the angle θ is 67 degrees and the length of the string (hypotenuse) is 150m, we can substitute these values into the equation:
sin(67°) = height/150m
To solve for the height, we can rearrange the equation:
height = sin(67°) * 150m
Using a scientific calculator, input sin(67) and multiply the result by 150:
height = sin(67°) * 150 ≈ 141.13m
Therefore, the height of the kite is approximately 141.13 meters.