Problema Solution
13. Find the area and perimeter of a triangle , two of whose sides are 7.5 cm and 13 cm. if their included angle is 42 degree 29 minutes.
Answer provided by our tutors
Use law of cosines to find the third side
c^2=a^2+b^2-2ab*cos(C)
c^2=7.5^2+13^2-[2*7.5*13*cos(42 29/60)]
c^2=225.25 - 195*cos(42.48333333333333333333333)
c^2=225 - 143.8073962
c^2=81.1926038
c=9.010693858
Perimeter = a + b + c = 7.5 + 13 + 9.010693858 = 29.51069386 units
Area (using Hero's formula):
Area(triangle) = sqrt[s(s-a)(s-b)(s-c)] where s is the semi-perimeter
s=(29.51069386)/2 = 14.7554
Area(triangle) = sqrt[s(s-a)(s-b)(s-c)]
=sqrt[14.7554(14.7554 - 7.5)(14.7554 - 13)(14.7554 - 9.010693858)
=sqrt[1079.583554]
=32.857o1682 units^2
Perimeter = 29.51069386 cm
Area = 32.857o1682 cm^2