Question

Help giving medals find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. b = 104°, a = 11 cm, c = 18 cm 192.12 cm2 96.06 cm2 23.95 cm2 99 cm2

Answer 1

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 2

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, $s=\frac{a+b+c}{2}=\frac{11+23.24+18}{2}=\frac{52.24}{2}=26.12$

$Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{26.12(26.12-11)(26.12-23.24)(26.12-18)}$

       $=\sqrt{26.12\times15.12\times2.88\times8.12}=\sqrt{9235.78}=96.02$

Area of the triangle = 96.02 cm²

Therefore, Option B is correct.