The Unknown Below the Bar
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 18 of 50.
When the side you want is the hypotenuse, it lands on the bottom of the ratio. The side next to a 40° angle is 8, and you want the hypotenuse x.
The board writes cos(40°) = 8/x. Bring x up first: moving it across gives x×cos(40°) = 8. Now x is multiplied by the number cos 40°, so divide both sides by it: x = 8/cos(40°), which rounds to 10.44.
The check is quick: 10.44 is longer than 8, as a hypotenuse must be. Dividing by the sine or cosine of an acute angle always makes the number bigger, because both are between 0 and 1.
Challenge
Triangle ABC has a right angle at C and a 25° angle at A. The side opposite the 25° angle is 6. Find the hypotenuse x, rounded 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