Question

Construct a triangle ABC in which BC = 7 cm, $\angle $B = $75^{\circ}$ and AB + AC = 13 cm.

Answer 1

Hint:
We will first draw the base BC = 7 cm of the required triangle. Then, we will measure angle B and construct it using the protractor as a ray BM. Then, we will measure the length 13 cm on our compass and mark it as N measuring from point B. Then, we will join the point N and C. We will draw a perpendicular bisector of the side DC. Marking the point where this perpendicular bisector of NC cuts the side BN as A and then we will join this point A to C. The required triangle will be constructed then.

Complete step by step solution:
We are required to construct a triangle ABC.
We are given that side BC = 7 cm.
The angle $\angle $B = 75° and the sum of sides AB and AC is given as 13 cm.
Step 1: We will first draw the base BC = 7 cm.

Step 2: We will construct angle B = $75^{\circ}$. Let the ray be BM.

Step 3: We will adjust the compass to the length equal to AB + AC = 13 cm. We will mark an arc of 13 cm from B on the ray BM. Let the arc cut BM at N.
Step 4: we will join C and N.

Step 4: now, we will draw a perpendicular bisector of CN and we will mark that point as A where the bisector cuts at BN.

Triangle ABC is the required triangle.

Note:
All you need to be careful is with while drawing the angle B and while marking the arc with the compass. You must have sharp pencil and a good compass. You need to be careful while drawing the perpendicular bisector. The length of the compass arc should be more than half of the side length while drawing a perpendicular bisector.