Question

Construct a triangle ABC, in which $\angle$B = 53.13°, $\angle$C = 36.87° and AB + BC+ CA = 24 cm. What type of triangle is this?

Answer 1

Steps-

-Draw line segment PQ of length 24 cm. From P draw ray PL which makes angle 53.13^∘ with PQ using a protractor. Similarly, draw ray QM which makes angle 36.87^∘ with PQ.

-Using angle bisector construction method, draw angle bisectors for angles APQ and angle AQP. Let these 2 angle bisectors meet at A.

-Using perpendicular bisector construction method draw perpendicular bisectors DE for AP and FG for AQ respectively.

-Let the point where DE meets PQ be B and let the point where FG meets PQ be C. Join AB and AC. The required triangle is triangle ABC, which is right - angled triangle.