A Leg Below the Bar
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 20 of 50.
A tangent can put the unknown on the bottom too, when the side you want is the adjacent leg. A building 12 m tall is seen at 40° from a point on the ground. How far is that point from the building?
The height is opposite 40° and the distance d is adjacent: tan(40°) = 12/d. Move d across and divide by tan 40°: d = 12/tan(40°), about 14.30 m. The tangent of 40° is below 1, so the distance comes out longer than the height, which fits an angle under 45°.
Challenge
Triangle PQR has a right angle at P and a 58° angle at Q. The side opposite the 58° angle is 14. Find the side x next to the 58° 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 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