How Tall Is the Tree?
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 1 of 50.
A tree casts a shadow 20 m long on flat ground. From the tip of the shadow, the sun's rays meet the ground at 37°. Nobody has to climb the tree with a tape measure: that one angle and that one length on the ground fix its height.
That is the whole idea of trigonometry. In a right triangle the angles decide the ratios of the sides, so an angle you can measure turns a length you can reach into a length you cannot. In this section you tap the sides of triangles, choose the ratio that links them, and solve the equation the board writes for you.
Challenge
The board already holds the tree's height h, worked out exactly from the 37° angle and the 20 m shadow. A height is only useful as a number of metres, so press Round to 2 decimal places. Then press Check.
Try it yourself
Solve for h
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 Ratios