![]() They would then construct a similar triangle as shown in figure (b), with the same angles at \(A\) and \(B\), and measure its sides. Two observers on the shore at points \(A\) and \(B\) would sight the ship and measure the angles formed, as shown in figure (a). In the sixth century BC, the Greek philosopher and mathematician Thales used similar triangles to measure the distance to a ship at sea. If Edo is 6 feet tall, what is his estimate for the height of the Washington Monument?Ģ3. From his physics class Edo knows that the angles marked and are equal. He is feet from the tip of the reflection, and that point is 1080 yards from the base of the monument, as shown below. He notices that he can see the reflection of the top of the monument in the reflecting pool. ![]() Edo estimates the height of the Washington Monument as follows. If she is 5 feet 6 inches tall, how high is the cliff?Ģ2. ![]() She then measures the distance to the mirror (2 feet) and the distance from the mirror to the base of the cliff (56 feet). The angles 1 and 2 formed by the light rays are equal, as shown in the figure. She places a mirror on the ground so that she can just see the top of the cliff in the mirror while she stands straight. A rock climber estimates the height of a cliff she plans to scale as follows. In Problems 15–20, use properties of similar triangles to solve for the variable.įor Problems 21–26, use properties of similar triangles to solve.Ģ1. Explain why this distance is the same as the distance across the river.įor Problems 7–10, decide whether the triangles are similar, and explain why or why not.Īssume the triangles in Problems 11–14 are similar. Add triangle \(ABC\) to your figure.Ĭ Finally, you can measure the distance from point \(A\) to point \(C\). Have a friend mark the spot \(C\) on the ground where the brim of your cap points. \) and sight along the bank on your side of the river.
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