CD is an altitude in right triangle ABC. The hypotenuse is 9 inches long, and ¯¯¯¯¯¯¯¯¯ AD is 5 inches long as shown below. What is the value of a? 7.5 inches 6.7 inches 6 inche…

Question

asked Jun 12, 2023 24.2k views

1 Answer

Ipsi · Answer 1 · 2023-06-18T08:02:14+0000

Answer:

a = 6 in

Explanation:

Using Pythagoras' Theorem
a^2+b^2=c^2 , where a and b are the legs, and c is the hypotenuse of a right triangle.

a^2+b^2=9^2

5^2+DC^2=b^2

4^2+DC^2=a^2

$\implies 4^2+DC^2+5^2+DC^2=9^2$

$\implies 2 \ DC^2 =40$

$\implies DC^2=20$

If
a^2=4^2+DC^2=16+20=36

$\implies a=√(36) =6$