a kite with a string 150 feet long makes an angle 45 with the ground, assuming the string is straight ,how high is the kite?
sin45 = h/150
h = 150*sin45 =
since a 45 degree right triangle has two equal sides, using pythagorean theorem,
150^2 = a^2 + a^2
2a^2 = 150^2
a = squareroot(150^2/2) = 75sqrt(2) feet = ~106.066 feet
To determine the height of the kite, we can use the basic trigonometric function of sine.
Sine (θ) = Opposite / Hypotenuse
In this case, the angle between the ground and the string is 45 degrees, and the length of the string (hypotenuse) is 150 feet. Let's label the height of the kite as "h."
So, using the formula:
sin(45°) = h / 150
To find the value of sine (45°), we can use the special right triangle, where the angles are 45°-45°-90°. In this triangle, the sides are in a ratio of 1:1:√2.
Therefore, sin(45°) = 1/√2 = √2/2.
Substituting this value into the equation:
√2/2 = h / 150
To solve for "h," we can cross multiply and find:
h = (√2/2) * 150
h = (√2 * 150) / 2
Simplifying further:
h = (150√2) / 2
h = 75√2
So, the height of the kite is approximately 75√2 feet.
To find the height of the kite, we can use trigonometry. Specifically, we will use the sine function.
Step 1: Draw a diagram to visualize the problem. Draw a right-angled triangle representing the situation. Let's denote the height of the kite as "h" and the angle made by the string with the ground as 45 degrees.
Step 2: Identify the relevant sides of the triangle. The string of the kite represents the hypotenuse of the triangle, which is 150 feet long. The height of the kite represents the opposite side to the given angle, and we need to find its length.
Step 3: Write down the formula for the sine function. In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. The formula for sine is:
sin(angle) = opposite/hypotenuse
Step 4: Substitute the given values into the formula. In this case, we have:
sin(45) = h/150
Step 5: Solve for the height of the kite. Rearrange the formula to solve for "h":
h = sin(45) * 150
Step 6: Calculate the height. Use a calculator to find the sine of 45 degrees, which is approximately 0.7071. Multiply this value by 150:
h ≈ 0.7071 * 150
h ≈ 106.07
The height of the kite is approximately 106.07 feet.