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Dmitry [639]
3 years ago
9

Help giving medals find the area of the triangle with the given measurements. round the solution to the nearest hundredth if nec

essary. b = 104°, a = 11 cm, c = 18 cm 192.12 cm2 96.06 cm2 23.95 cm2 99 cm2
Mathematics
2 answers:
FromTheMoon [43]3 years ago
8 0

In order to solve for the area of the triangle with the given dimensions, we use the equation

<span>                        A = ac(cos b)/2</span>

Substituting the known values,

<span>                         A = (11 cm)(18 cm)(cos 104o)/2 = 23.95 cm2</span>

 

<span>Thus, the answer is the third choice. </span>

Marysya12 [62]3 years ago
6 0

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.

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