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Question Video: Using Right Triangle Trigonometry to Solve Word Problems Mathematics • Third Year of Preparatory School

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A kite, which is at a perpendicular height of 44 m, is attached to a string inclined at 60° to the horizontal. Find the length of the string accurate to one decimal place.

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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.

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