Question

Construct a triangle abc whose perimeter is 8.2 cm and the base angle are 45 degree and 60 degree

Answer 1

Answer:

Given: The Perimeter of the triangle and two angles are known to us.

Requirements: A ruler, a protractor and a compass.

Step-by-step explanation:

Let us consider a triangle ABC, whose perimeter is 8.2 cm and the two given angles be 45∘ and 60∘

Thus A+B+C = 8.2 cm ,

∠B=45∘

∠C=60∘

The steps for its construction are:

Construction:

• Draw a line segment XY of length AB + AC + BC, that is, 18 cm.

• From the point X, using the protractor construct ∠LXY which is equal to ∠B, that is, 45°.

• From the point Y, construct ∠MYX which is equal to ∠C, that is, 60°.

• Using the compass, construct the bisectors of ∠LXY and ∠MYX. Mark the point as A where the constructors meet.

• Construct the perpendicular bisector of AX and name it as PQ.

• Construct the perpendicular bisector of AY and name it as RS.

• Let PQ meet XY at B and RS meet XY at C.

• Join the points A and B as well as A and C.

You get the ∆ABC of the required measurements.