Question

construct a triangle ABC in which perimeter of the triangle= 11.5 cm and the base angles are 45 degree and 60 degree. ​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

The sides a, b and c total to 11.5

The 3 angles are A = 45 degrees, B = 60 degrees and C = 75 degrees.

So the longest side ( opposite angle C) is side c.

a + b + c = 11.5

By the Sine Rule

a / sin A = b / sin B = c / sin C

a/sin 45 = c / sin 75

so a = c sin 45 / sin 75

b /  sin 60 = c / sin 75

so b = c sin 60 / sin 75

So we have:

c + a + b = 11.5

c +  c sin 45 / sin 75 + c sin 60 / sin 75 = 11.5

2.6286c = 11.5

c =  4.375.

So to construct the triangle

Draw a line c ( ie AB) of length  4.4 cm .

Using a protractor draw a line from A at an angle of 45 degrees.

Using a protractor draw a line from B at an angle of 60 degrees.

Where these lines cross is the point C of triangle ABC.