Question

PLEASE HELP ASAP!

1. In ΔABC, m∠A = 90° and AN is an altitude. If AB = 20 in and AC = 15 in, find BC, BN, NC, AN.


2. In the ΔABC, AB = 16 in, BC = 9 in, AC = 10 in. AD ⊥ to the extended BC. Find CD.

Answer 1

2= 4 1/6

Explanation:

draw the diagram and extend BC to D

draw AD

use the Pythagorean Theorem with triangle ADC

call AD "h"

call DC "x"

h2+x2=102

now use the Pythagorean Theorem with triangle ADB

AD=h, AB=16, DB=(x+9)

h^2+(x+9)^2=16^2

from the first equation get h^2=10^2-x^2

from the second equation get h^2=16^2-(x+9)^2

set the two right sides equal to each other because they both equal h2

10^2-x^2=16^2-(x+9)^2

100-x^2=256-x^2-18x-81

cancel -x2 from both sides

100=256-18x-81

100=175-18x

100-175=-18x

-75=-18x

18x=75

x=75/18

x=4.1666... inches or 4 1/6 inches for the length of DC