Applications of Right Triangles

Pre-Calculus · Axiom Academy

LESSON Applications of Right Triangles Heights you can't reach, distances you can't pace off — find them by building one right triangle and picking the matching ratio. 1. Angle of Elevation: How Tall Is the Tree? The angle of elevation is the angle from a horizontal line of sight up to an object above you. Stand back a measured distance, sight the top, read the angle off — and the situation becomes a right triangle whose vertical leg is the height you want. You stand 40 ft from the base of a tree on level ground and measure the angle of elevation to its top as 50° . How tall is the tree? 40 ft is ADJACENT to the angle; the height is OPPOSITE → use tangent 2. Angle of Depression: Finding a Boat's Distance Now look down . The angle of depression is measured from a horizontal line of sight down to something below you. The catch beginners miss: it is not an angle inside the triangle — it sits up at the top, between your horizontal and your line of sight. From the top of a 60 ft lighthouse you spot a boat at an angle of depression of 40° . How far is the boat from the base of the lighthouse? 3. A Ladder on a Wall: Cosine and Sine Tangent isn't always the right tool. When you know the hypotenuse — the slanted distance — cosine and sine take over. A leaning ladder is the classic case: the ladder itself is the hypotenuse, and we want both how far its base sits from the wall and how high it reaches. Adjacent to the 70° angle, hypotenuse known cosine: .

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