1. Find the exact value for area of the triangle with the side lengths 5, 9, and 10.

area = 6  units²

Step-by-step explanation:

Given the 3 sides of a triangle, we can use Hero's formula to calculate the area (A)

A =

where s s the semi perimeter and a, b , c the sides of the triangle

let a = 5, b = 9 and c = 10

s = = = = 12

A =

   =

   =

   =

   =  6 units²

Step-by-step explanation:

a = 5 units ; b = 9units ; c = 10 units

Semi perimeter = (a+b+c)/2 = (5+9+10)/2 = 24/2 = 12 units

s-a = 12 -5 = 7 units

s -b = 12 - 9 = 3 units

s-c = 12- 10 =2 units

=6*3.742 = 22.452

= 22.45 square units

  21.3

step-by-step explanation:

multiplying the given equation by c/sin(25°), we get

  c = 9/sin(25°) ≈ 21.2958 ≈ 21.3

we assume "c" is the length of ab, the side opposite angle c in triangle abc.