Video Transcript
A kite, which is at a perpendicular
height of 44 meters, is attached to a string inclined at 60 degrees to the
horizontal. Find the length of the string
accurate to one decimal place.
Let’s begin by drawing a sketch of
this problem. We have a kite which is attached to
a string. This string is inclined at an angle
of 60 degrees to the horizontal and the perpendicular height of the kite. So that means the height of the
kite that makes a right angle with the horizontal is 44 meters. We can now see that we have a right
triangle formed by the horizontal, the vertical, and the string of the kite. We want to calculate the length of
the string, so let’s label that as 𝑦 meters. We’re working with a right
triangle, so we can approach this problem using trigonometry.
We’ll begin by labeling the three
sides of the triangle in relation to the angle of 60 degrees. Next, we’ll recall the acronym
SOHCAHTOA to help us decide which trigonometric ratio we need here. The side whose length we know is
the opposite, and the side we want to calculate is the hypotenuse. So we’re going to be using the sine
ratio. For an angle 𝜃 in a right
triangle, this is defined as the length of the opposite divided by the length of the
hypotenuse. We can then substitute the values
for 𝜃, the opposite and the hypotenuse, into this equation giving sin of 60 degrees
equals 44 over 𝑦.
We need to be careful because the
unknown appears in the denominator of this fraction. Next, we solve this equation. As 𝑦 appears in the denominator,
the first step is to multiply both sides of the equation by 𝑦, which gives 𝑦 sin
60 degrees is equal to 44. Next, we divide both sides of the
equation by sin of 60 degrees, giving 𝑦 equals 44 over sin of 60 degrees. And then we evaluate on our
calculators, which must be in degree mode, giving 50.806. The question asks for our answer
accurate to one decimal place. So we round this value and include
the units which are meters. The length of the string to one
decimal place is 50.8 meters.
