Triangle SAS

Calculate the area and perimeter of a triangle if two sides are 46 m and 33 m long and the angle between them is 170°.

Final Answer:

A =  131.799 m
o =  157.7075 m

Step-by-step explanation:

a=46 m b=33 m γ=170 ∘   sin γ = h:b  h=b⋅ sinγ=b⋅ sin170° =33⋅ sin170° =33⋅ 0.173648=5.73039 m  A=2a⋅ h​=246⋅ 5.7304​=131.799 m
a1​+a2​=a cos γ = a1​:b  a1​=b⋅ cosγ=b⋅ cos170° =33⋅ cos170° =33⋅ (−0.984808)=−32.49866 m a2​=a−a1​=46−(−32.4987)≐78.4987 m  c2 = h2 + a22​  c=h2+a22​​=5.73042+78.49872​≐78.7075 m  o=a+b+c=46+33+78.7075=157.7075 m

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You need to know the following knowledge to solve this word math problem:

arithmeticplanimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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