Question

what is the ratio of sides of a triangle with angle 45°, 60°, 75°

• A. 1 : 2 : 3
• B. √2 : √3 : 1
• C. 2 : 6 : √3
• D. 2 : √6 : 1 + √3

Answer 1

Answer:

D. 2 : √6 : 1 + √3

Cut triangle ABC into 2 by drawing a perpendicular through angle ACB

So we get two triangles ACD with angles 30° 60° 90° and triangle BDC with angles 45° 45° 90°

We know that,

ratio of sides of a triangle with angles 45°, 45°, 90° is 1 : 1 : √2

and, ratio of sides of triangle with angle 30, 60, 90 is = 1 : √3 : 2

So the ratio of sides triangle ABC is 2/√3 : √2 : 1 + 1/√3

= 2 : √2√3 : √3 + 1

= 2 : √6 : 1 + √3