The area of the triangle rounded to the nearest tenth is 33.3 squared inches.
What is the area of the triangle?
Given the data in the diagram;
First we find the dimension of side b.
From the rule of cosines.
b = √[ a² + c² - 2acCosB ]
We substitute into the formula.
b = √[ 7² + 13² - ( 2 × 7 × 13 × cos( 133° ) ]
b = √[ 49 + 169 - ( 182 × cos( 133° ) ) ]
b = √[ 218 - 182×cos( 133° ) ]
b = √[ 342.1237 ]
b = 18.5
Next, we find angle C.
From rule of cosines.
cosC = [ b² + a² - c² ] / 2ba
cosC = [ 18.5² + 7² - 13² ] / [ 2 × 18.5 × 7 ]
cosC = [ 342.25 + 49 - 169 ] / [ 259 ]
cosC = [ 222.25 ] / [ 259 ]
cosC = [ 0.8581 ]
C = cos⁻¹[ 0.8581 ]
C = 30.9°
Now, we can find the area of the triangle.
Area = [ ab × sinC ] / 2
Area = [ 7 × 18.5 × sin( 30.9 ) ] / 2
Area = [ 129.5 × 0.51354 ] / 2
Area = 66.5 / 2
Area = 33.3 in²
The area of the triangle rounded to the nearest tenth is 33.3 squared inches.
Learn about cosine rule here: brainly.com/question/20839703
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