Let A = (6,0), B = (0,8),C = (0,0). In triangle ABC, let F be the foot of the altitude drawn from C to side AB. (a) Explain why the angles of triangles ABC, CBF, and ACF are the same. (b) Find coordinates for F, and use them to calculate the exact lengths FA, FB, and FC. (c) Compare the sides of triangle ABC with the sides of triangle ACF. What do you notice?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let A = (6, 0), B = (0,8), C = (0,0). In triangle ABC, let F be the foot of the altitude drawn from C to side AB.
(a) Explain why the angles of triangles ABC, CBF, and ACF are the same.
(b) Find coordinates for F, and use them to calculate the exact lengths FA, FB, and FC.
(c) Compare the sides of triangle ABC with the sides of triangle ACF. What do you notice?
Transcribed Image Text:Let A = (6, 0), B = (0,8), C = (0,0). In triangle ABC, let F be the foot of the altitude drawn from C to side AB. (a) Explain why the angles of triangles ABC, CBF, and ACF are the same. (b) Find coordinates for F, and use them to calculate the exact lengths FA, FB, and FC. (c) Compare the sides of triangle ABC with the sides of triangle ACF. What do you notice?
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