Question

Give the simplified radical form for each side length requested.

Pls answer only if you can explain and if your sure it’s the right answer.

I need help in understanding how to work it myself so please make sure you explain well.

Answer 1

• See below

Explanation:

30×60×90 right triangle has side ratios as:

• s : l : h = 1 : √3 : 2, where s- short leg, l - long leg, h - hypotenuse

45×45×90 right triangle has side ratios as:

• l : l : h = 1 : 1 : √2, where l- legs, h- hypotenuse

If you know one of the sides its easy to find the missing ones.

a) 30×60×90 right triangle

• Given l = 12

• s : 12 : h = 1 : √3 : 2

• CB = s = 12 / √3 = 12√3/3 = 4√3
• AB = h = 2s = 2*4√3 = 8√3

b) 45×45×90 right triangle

• Given l = √22

• BC = l = √22
• AB = l√2 = √22×√2= √44 = 2√11

c) 30×60×90 right triangle

• Given h = 20√6

• s : l : 20√6 = 1 : √3 : 2

• BC = s = h/2 = 20√6/2 = 10√6
• AC = l = s√3 = 10√6×√3 = 10√18 = 10×3√2 = 30√2