Construct a isosceles triangle with base 5.8 cm and verticle angle is 75 degree

Question

Construct an isoselceles triangle whose base is 5.8 cm and whose vertical angle is 75°

Answer 1

Steps of construction:  

1. Draw a line segment BC of length 5.8 cm 

2. Draw a ray BX such that ∠CBX = 52.5°  [Since vertical angle is 75° then the two equal angles should be 52.5° each] 

3. Now draw another ray CY such that ∠BCY = 52.5° 

4. Mark the point of intersection of two rays as A. ABC is the required isosceles triangle.

Comments

In geometric construction it is customary to draw the angle with the help of compass and ruler only. Here the traces of construction of 52.5° angle should be shown.

Answer 2

Here is the construction with required traces of construction

Steps followed

1) A line segment AB of length 5.8 cm is drawn

2) Angle BAD =105° is drawn with the help of a ruler and a compass..

3) AC the bisector of angle BAD is drawn.

Now angle CAB = angle CAD=52.5°

4) Angle ABC=angle CAB is drawn.

5)ABC triangle formed becomes required triangle as angle ACB=75° and AB=5.8cm.