a kite with a string 150ft long makes an angle of 45 degree with the ground. assuming that the string is straight how high is the kite?
h/150 = sin 45°
To find the height of the kite, we need to use trigonometry, specifically the sine function. Let's break down the problem into smaller steps:
Step 1: Understand the given information:
- The string length is 150 feet
- The angle between the string and the ground is 45 degrees
Step 2: Identify the triangle:
In this case, we have a right triangle. One of the angles is 90 degrees because the string is assumed to be straight. The angle between the string and the ground is 45 degrees. The side of the triangle opposite to the 45-degree angle represents the height of the kite.
Step 3: Apply trigonometry:
We can use the sine function to find the height (opposite side) of the triangle:
sin(angle) = opposite/hypotenuse
In this case:
sin(45 degrees) = height/150 feet
Step 4: Solve for the height:
To find the height, multiply both sides of the equation by 150 feet:
height = sin(45 degrees) * 150 feet
Step 5: Calculate the height:
Using a calculator, we can find the value of sin(45 degrees) which is approximately 0.7071.
Now, substitute this value into the equation:
height = 0.7071 * 150 feet
Calculating this gives us:
height ≈ 106.06 feet
Therefore, the height of the kite is approximately 106.06 feet.