Mathematics — first biennium · Lesson
Solving a triangle means finding missing measures from sufficient data. In a right triangle, one length and a trigonometric ratio can determine the other sides.
Prerequisites: Trigonometric ratios and Pythagoras
Goal: Find missing sides from a hypotenuse and trigonometric ratios and verify the result with Pythagoras.
In this lesson: Find missing sides from a hypotenuse and trigonometric ratios and verify the result with Pythagoras.
New concept: Solving a triangle means determining its missing measures. In a right triangle, choose the trigonometric ratio containing the known side and the unknown side; the other acute angle is 90° minus the first.
How to proceed: Multiply the hypotenuse by each ratio. At the end verify that the two legs satisfy a²+b²=c².
You can already assume: Trigonometric ratios and Pythagoras.
The triangle shows the sides obtained from the trigonometric ratios; Pythagoras provides an independent final check.
Completed exercises: 0/5 · Correct on first attempt: 0
Multiply the hypotenuse by each ratio. At the end verify that the two legs satisfy a²+b²=c².
Data / situation: A right triangle has hypotenuse 39, sin α=12/13 and cos α=5/13. Find the two legs relative to α.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.