Review probs: For right triangle ABC, if AC = 4 and....

[daniellagirl89]

I need some help with some review problems in Algebra 2


41: For a right triangle ABC with right angle C, if AC = 4 and AB = 5, what is the length of BC in simplified form?

31:
√15 √3 + √15 2√5

 

[jwpaine]

For a right triangle ABC with right angle C, if AC = 4 and AB = 5, what is the length of BC in simplified form?

Use the pythagorean theorem \(\displaystyle \L a^2 + b^2 = c^2\)

let AB = c, AC = a, BC = b

to find b:

\(\displaystyle \L b^2 = c^2 - a^2\)

square root both sides:

\(\displaystyle \L b = \sqrt{c^2 - a^2} = \sqrt{5^2 - 4^2} = ?\)

See?

31:
√15 √3 + √15 2√5

\(\displaystyle \L \sqrt{15}\cdot \sqrt{3} + \sqrt{15} \cdot 2\sqrt{5} =\)

\(\displaystyle \sqrt{15\cdot3} + 2\sqrt{5\cdot15} =\)

\(\displaystyle 3\sqrt{5} + 2\cdot5\sqrt{3} =\)

\(\displaystyle 3\sqrt{5} + 10\sqrt{3}\)

Hope this helps!

John