A kite and a height of 75 meters from the ground is attached to a string inclined at 60 degrees to the horizontal. How do you find the length of the string to the nearest meter?
the easy way is to remember that the sides of a 30-60-90 triangle are in the ratio
1:√3:2
You have a long side of 75, so the other two sides are
75/√3,75,150/√3
The string is the long side.
Or, using trig, the length of the string, x, is found using
75/x = sin 60°
I divided sin 60 degrees and 75 and got 0.0115.
Didn't that answer strike you as totally unreasonable?
How can the kite-string be only 1 cm long ??
Steve told you : 75/x = sin 60°
so x sin60 = 75
x = 75/sin60 = appr 86.6 metres
Yes it did. I just wasn't familiar with the concept but thanks.
Oh the mistake was me putting sin60 over 75. I understand the concept.
To find the length of the string, we can use trigonometric functions. In this case, we need to use the sine function.
Step 1: Identify the given information:
- The height of the kite from the ground is 75 meters.
- The angle between the string and the horizontal is 60 degrees.
Step 2: Understand the trigonometric relationship:
The sine function relates the lengths of the sides of a right-angled triangle. In this case, the sine function relates the opposite side (the height of the kite) to the hypotenuse (the length of the string). The formula to find the length of the string is:
sin(angle) = opposite/hypotenuse.
Step 3: Substitute the known values into the formula:
sin(60°) = 75 meters/hypotenuse.
Step 4: Solve for the length of the string (hypotenuse):
To find the length of the string, we rearrange the formula to isolate the hypotenuse:
hypotenuse = opposite/sin(angle).
hypotenuse = 75 meters / sin(60°).
hypotenuse ≈ 86.60 meters.
Therefore, the length of the string, to the nearest meter, is approximately 87 meters.