Question

Find the area of triangle ABC.

A. 35.92 units²
B. 43.79 units²
C. 21.39 units²
D. 22.91 units²

Answer 1

`\text{C. }21.39\:\mathrm{units^2}`

Explanation:

The area of a triangle with sides
`a` and
`b` and angle
`\gamma` between them is given by
`A=(1)/(2)ab\sin \gamma`.

Therefore, in the given triangle, we want to find two sides with the angle between them given. In this case, the angle between the two sides 7.39 and 9.75 is marked as
`36.43^(\circ)`. Assign values:

• 
  `a\implies 7.39`
• 
  `b\implies 9.75`
• 
  `\gamma \implies 36.43^(\circ)`

Substituting these values into our area formula, we get:

`A=(1)/(2)\cdot 7.39\cdot 9.75\cdot \sin (36.43)^(\circ),\\A=21.3938371858,\\A\approx \boxed{21.39\:\mathrm{units^2}}`