find the measure of each angle of the triangle

Question

the lengths of a triangle measure 27, 46 and 67 cm.

Answer 1

the lengths of a triangle measure a = 27,b = 46 and c = 67 cm.

use the low of cosines formula cosA = b² +c² - a²/2bc.

Substitute a = 27,b = 46 andc = 67 in the above equation.

cosA  = (46^2 + 67^2 - 27^2)/2(46)(67)

cosA  = (2116 + 4489 - 729)/6164

cosA  = (6605-729)/6164

cosA  = 5876/6164

cosA  = 0.953

cosB =a² +c² -b² /2ac = 0.857

cosC =a² +b²- c² /2ab = -0.661

Comments

The angles are 17.58^o, 30.98^o and 131.44^o.

Answer 2

The lengths of a triangle measure a = 27,b = 46 and c = 67 cm.

Use the low of cosines formula cosA = [ b² +c² - a² ] / 2bc.

Substitute a = 27, b = 46 and c = 67 in the above equation.

cos A = [(46)² + (67)² - (27)] / 2bc

cos A  = (46^2 + 67^2 - 27^2)/2(46)(67)

cos A  = (2116 + 4489 - 729)/6164

cos A  = (6605-729)/6164

cos A  = 5876/6164

cos A ≅ 0.953277

A ≅ cos^{- 1}(0.953277) ≅ 17.58^o.

 

Find angle B : a = 27, b = 46 and c = 67

cos B = [ a² + c² - b² ] / 2ac

cos B = [ (27)² + (67)² - (46)² ] / 2(27)(67)

cos B = [ 729 + 4489 - 2116 ] / 3618

cos B = 3102 / 3618

cos B ≅ 0.85737976

B ≅ cos^{- 1}(0.85737976) ≅ 30.98^o.

 

Find angle C : a = 27, b = 46 and c = 67

cos C = [ a² + b² - c² ] / 2ab

cos C = [ (27)² + (46)² - (67)² ] / 2(27)(46)

cos C = [ 729 + 2116 - 4489 ] / 2484

cos C = - 1644 / 2484

cos C ≅ - 0.6618357487

C ≅ cos^{- 1}(- 0.6618357487) ≅ 131.44^o.

The angles are 17.58^o, 30.98^o and 131.44^o.