A kite flying at a height of 55m is attached to a string which makes an angle of 55 degrees with the horizontal. What is the length of the string
as always, draw a diagram and review your basic trig functions. You will see that
55/x = sin55°
sin55=55/x
xsin55=55
x=55/sin55
x=67.14
Always draw a diagram to see what is happening.
Using trigonometry: SOH is used
sin(55)=opposite/hypotenuse
=55m/hypotenuse
Hyp(sin55) =55m
Hyp= 55m/sin55
Hypotenuse= 67.14 metres (2 decimal places)
Always draw a diagram to see what is happening.
Using trigonometry: SOH is used
sin(55)=opposite/hypotenuse
=55m/hypotenuse
Hyp(sin55) =55m
Hyp= 55m/sin55
Hypotenuse= 67.14 metres (2 decimal places)
To find the length of the string, we can use trigonometry.
Let's consider the triangle formed by the kite, the ground, and the string. In this triangle, the height of the kite is the opposite side, and the length of the string (which we are trying to find) is the hypotenuse. The angle between the string and the horizontal is the angle formed between the hypotenuse and the base.
Using the definition of sine, we can write:
sin(angle) = opposite / hypotenuse
Applying it to our triangle, we have:
sin(55 degrees) = 55m / hypotenuse
Now, to find the hypotenuse (length of the string), we can isolate it in the equation:
hypotenuse = 55m / sin(55 degrees)
Using a calculator, we can find the value of sin(55 degrees) ≈ 0.8192, and then substitute it into the equation:
hypotenuse = 55m / 0.8192
Calculating this, we find:
hypotenuse ≈ 67.16m
Therefore, the length of the string is approximately 67.16 meters.