Is the Answer Sensible?
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 21 of 50.
A trig answer can be checked without redoing it. Three questions catch most slips. Is the hypotenuse the longest side? Is the leg opposite the bigger acute angle the longer leg? Does the size fit the story?
A loading ramp rises 0.5 m at an angle of 5°. Its length is 0.5/sin(5°), about 5.74 m. That is more than eleven times the rise, which fits a ramp that gentle. Had you multiplied instead, 0.5 sin 5° is about 0.04 m, a ramp shorter than its own rise: impossible, so the slip shows at once.
Challenge
A ramp up to a stage rises 1.2 m and makes an 8° angle with the floor. How long is the ramp? Find x to two decimal places, and check that it is longer than the rise. 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