Video narration
How can you find a wall's height-or even a tree's-without climbing it? Use a ladder leaning against the wall. The ladder, wall, and ground form a right triangle. Choose the angle where the ladder meets the ground. From that angle, the wall height is opposite, the ground distance is adjacent, and the ladder is the hypotenuse. Here is the key turn: the triangle is not just a shape. Once the angle is fixed, the relationships between its sides are fixed too. These relationships are trigonometry's three basic ratios: sine compares opposite to hypotenuse, cosine compares adjacent to hypotenuse, and tangent compares opposite to adjacent. If you know an angle and one side, choose the ratio that matches the known and needed sides. That ratio turns the triangle into a calculation. Measure an angle and one side, choose sine, cosine, or tangent, and calculate the tree's height without climbing it.