Tangent: Leg From Leg
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 14 of 50.
When the hypotenuse is not involved at all, the tangent does the job. You stand 7 m from a flagpole and the top is 50° above the ground at your feet. The height is opposite 50°, the 7 m is adjacent, and the ratio of the two legs is the tangent.
The board writes tan(50°) = h/7. Multiply by 7: h = 7tan(50°), which rounds to 8.34. A tangent above 1 means the opposite leg is longer than the adjacent one, which happens for every angle above 45°: here the pole is taller than your distance from it.
Challenge
Triangle ABC has a right angle at C and a 41° angle at A. The side next to the 41° angle is 24. Find the side x opposite the 41° angle, 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 Sides2The Three Ratios
The Sine RatioThe Cosine RatioThe Tangent RatioChoosing the RatioRecap: The Three Ratios3Finding a Side
Sides at Any AngleRounding the AnswerTangent: Leg From LegA Ladder Against a WallThe Other Acute AngleRecap: Finding a Side6Special Triangles, Exactly
The Two Special TrianglesAn Exact HypotenuseThe Side Next to 30°An Exact AngleRecap: Exact Values