In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ah=hc+2 and bc=2, find hc.

  HC = 1

Step-by-step explanation:

AC = HC +AH = HC +(HC+2) = 2·HC +2

The altitude divides the triangle into similar triangles, so the ratio of hypotenuse to short side is the same for all. That is ...

  BC/HC = AC/BC

  2/HC = (2HC +2)/2

  4 = 2(HC)(HC +1) . . . . . cross multiply

  0 = HC² +HC -2 . . . . . . divide by 2, subtract 2

  0 = (HC -1)(HC +2) . . . . factor. Solutions are those values of HC that make the factors be zero.

The useful solution is ...

  HC = 1

its electric no smoke

step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.