ACT-Style: Right Triangle Trig Application

ACT Math · Axiom Academy

EXAMPLE ACT-Style Right Triangle Trig Application Using an angle of elevation and the tangent ratio to find a building's height From a point 150 feet from the base of a building, the angle of elevation to the top of the building is . What is the height of the building? (Round to the nearest foot.) Nicely done. You turned a word problem into a right triangle and picked the trig ratio that matched the sides you had. Draw the triangle first: the angle of elevation is measured up from the horizontal ground, so the horizontal distance is the adjacent side and the height is the opposite side. Match the ratio to the sides: opposite over adjacent is , so . On the ACT, "ladder," "ramp," "angle of elevation," and "shadow" problems are all the same move: sketch the right triangle, tag the sides as opposite / adjacent / hypotenuse, and let SOH-CAH-TOA pick the ratio.

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