Determine the area a triangle to the nearest square unit LT = 31.7o, r = 9.4, 5 = 13.1

Question

Determine the area of each triangle using the given information. Give answers to the nearest square unit. 

1. LT = 31.7o, r = 9.4, 5 = 13.1 

2. LM = 62.5°, K = 17.7,1 = 18.3 3. p = 7.4, s = 9.3, 1 = 14.5 

4. x = 8.7, y = 11.6, k = 19.2 

 

Answer 1

Question very unclear to me, so here is my try

1) r = 9.4

s= 13.1

Using cosine law:

t = sqrt( 9.4² + 13.1² + 2(9.4)(13.1)cos(31.7) ) = 7.1

Using Heron's formula

semi-perimeter, sp = (r+s+t)/2  = 14.8

Area = sqrt(sp(sp-r)(sp-s)(sp-t) = 32.344 sq units

2) k = 17.7

l = 18.3

Using cosine law:

m = sqrt( 17.7² + 18.3² + 2(17.7)(18.3)cos(62.5) ) = 18.68

Using Heron's formula

semi-perimeter, sp = (17.7+18.3+18.68)/2 = 27.19

Area = sqrt(sp(sp-k)(sp-l)(sp-m) = 141.91 sq units

 

3) p = 7.4, s= 9.3, l = 14.5

semi-perimeter, sp = (7.4 +9.3 +14.5)/2 = 15.6

Area = sqrt(15.6(15.6-7.4)(15.6-9.3)(15.6-14.5)) = 29.774 sq units

4) x= 8.7, y = 11.6, k = 19.2

semi-perimeter = (8.7+11.6+19.2)/2 = 19.75

Area = sqrt(19.75(19.75-8.7)(19.75-11.6)(19.75-19.2))  = 31.277 sq units