Question

Draw a triangle ABC, with AC = 4 cm, BC = 3 cm and ∠C = 105°. Measure AB. Is (AB)² = (AC)²  + (BC)²? If not which one of the following is true:

(AB)² > (AC)² + (BC)² or (AB)² < (AC)² + (BC)²?

Answer 1

Draw △ABC as shown in the figure with following steps.

Draw a line BC = 3 cm.

At point C, draw a line at 105° angle with BC.

Take an arc of 4 cm from point C, which will cut the line at point A.

Now, join AB, which will be approximately 5.5 cm.

AC² + BC² = 4² + 3² 

= 9 + 16

= 25

AB² = 5.52 = 30.25

AB² is not equal to AC²+ BC²

Therefore we have

AB² > AC² + BC²