a kite with a string 150 feet makes an angle of 45° with the ground. assuming the string is straight, how high is the kite?
h=150sin45
.106
To find the height of the kite, we can use trigonometry.
In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
In this case, the angle between the string and the ground is 45°, and the length of the string is 150 feet. Let's call the height of the kite "h."
Using sine:
sin(45°) = h / 150
Now we can solve for h:
h = sin(45°) * 150
Calculating sin(45°):
sin(45°) = √2 / 2
Substituting the value of sin(45°):
h = (√2 / 2) * 150
h = (1.414 / 2) * 150
h ≈ 1.414 * 75
h ≈ 106.06
Therefore, the kite is approximately 106.06 feet high.
To determine the height of the kite, we can use trigonometry, specifically the sine function. The sine function relates the ratio of the opposite side to the hypotenuse in a right-angled triangle.
In this case, the opposite side is the height of the kite and the hypotenuse is the length of the string.
Given that the angle between the string and the ground is 45° and the length of the string is 150 feet, we can use the equation:
sin(angle) = opposite / hypotenuse
Plugging in the values:
sin(45°) = height / 150 feet
Now, we need to find the value of sin(45°). The sine of 45° is equal to √2 / 2 or approximately 0.7071.
0.7071 = height / 150 feet
To isolate the height, we rearrange the equation:
height = 0.7071 * 150 feet
Evaluating the expression:
height ≈ 106.07 feet
Therefore, the height of the kite is approximately 106.07 feet.