SOLUTION: Let A=(6,0), B=(0,8), and C=(0,0). In triangle, ABC let F be the point of intersection of the altitude drawn from C to side AB. a. Explain why the angles of triangles ABC, CBF,

Algebra ->  Formulas -> SOLUTION: Let A=(6,0), B=(0,8), and C=(0,0). In triangle, ABC let F be the point of intersection of the altitude drawn from C to side AB. a. Explain why the angles of triangles ABC, CBF,       Log On


   

Question 1196423: Let A=(6,0), B=(0,8), and C=(0,0). In triangle, ABC let F be the point of intersection of the altitude drawn from C to side AB.
a. Explain why the angles of triangles ABC, CBF, and ACF are congruent
b. Find the coordinates of F and use them to calculate the exact lengths of FA, FB, and FC.
c. Compare the sides of triangle ABC with sides ACF. What do you notice?



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Diagram

Hints:
  • red angle + blue angle = 90 degrees
  • This fact allows us to prove the red angles are the same, and the blue angles are the same; therefore, the three right triangles (ABC, CBF, ACF) are similar triangles
  • the equation of line AB is 4x+3y = 24
  • the equation of line CF is -3x+4y = 0
  • Use those two equations to find the location of point F