In triangle ABC, where m<C, the altitude from <C drawn, how can you justify?

Question

a. Justify: AB/CB = CB/NB

b. Justify: AB/AC = AC/AN

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Answer 1 · 2018-04-21T12:54:04

See below.

a.

Looking at triangle ABC, with hypotenuse AB.

#cos(B)=(CB)/(AB)#

Looking at triangle CBN, with hypotenuse CB.

#cos(B)=(NB)/(CB)#

#:.#

#(CB)/(AB)=(NB)/(CB)#

Rearranging:

#(CB)/(NB)=(AB)/(CB)#

b.

Looking at triangle ABC, with hypotenuse AB.

#sin(B)=(AC)/(AB)#

Looking at triangle CBN, with hypotenuse CB.

#sin(B)=(CN)/(NB)#

#:.#

#(AC)/(AB)=(CN)/(NB)#

Rearranging:

#(AB)/(AC)=(AC)/(AN)#