In order to solve for the area of the triangle with the given dimensions, we use the equation
A = ac(cos b)/2
Substituting the known values,
A = (11 cm)(18 cm)(cos 104o)/2 = 23.95 cm2
Thus, the answer is the third choice.
Answer:
Option B is correct.
Step-by-step explanation:
Given: In a ΔABC, ∠B = 104° , a = 11 cm and c = 18 cm.
To find: area of the triangle.
We first find value of b using Law of cosines then using herons formula we find area of triangle.
Law of Cosines is a result used for calculating one side of a triangle when the angle opposite and the other two sides are known.
b² = a² + c² - 2ac × cos B
b² = 11² + 18² - 2 × 11 × 18 × cos 104°
b² = 445 - 396 × ( -0.24 )
b² = 540.04
b = 23.24 (nearest tenth)
Now, Herons Formula,
Semi perimeter, [tex]s=\frac{a+b+c}{2}=\frac{11+23.24+18}{2}=\frac{52.24}{2}=26.12[/tex]
[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{26.12(26.12-11)(26.12-23.24)(26.12-18)}[/tex]
[tex]=\sqrt{26.12\times15.12\times2.88\times8.12}=\sqrt{9235.78}=96.02[/tex]
Area of the triangle = 96.02 cm²
Therefore, Option B is correct.
