How Long Is the Kite String?
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 19 of 50.
The hypotenuse turns up in stories as the slanted thing: a kite string, a ramp, a rope, a ladder. A rope runs from the top of a mast to a peg 3 m from its foot and makes 62° with the ground. How long is the rope?
The 3 m along the ground touches the 62° angle at the peg: adjacent. The rope is the hypotenuse. So cos(62°) = 3/r, and r = 3/cos(62°), about 6.39 m. Draw the picture, mark the right angle where the upright meets the ground, then name the sides from the angle you know.
Challenge
A kite string is held at H and runs to the kite at K. The point G on the ground straight under the kite is 10 m from H, and the string makes a 55° angle with the ground. How long is the string? Find x to two decimal places. Then press Check.
Try it yourself
Use the figure to find x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Right-Triangle Trigonometry
1Sides of a Right Triangle
How Tall Is the Tree?The HypotenuseThe Opposite SideThe Adjacent SideWhen the Angle MovesRecap: Naming the Sides4Finding the Hypotenuse
The Unknown Below the BarHow Long Is the Kite String?A Leg Below the BarIs the Answer Sensible?Recap: The Hypotenuse2The Three Ratios
The Sine RatioThe Cosine RatioThe Tangent RatioChoosing the RatioRecap: The Three Ratios