SAS calculation

Given the triangle ABC, if side b is 31 ft., side c is 22 ft., and angle α is 47°, find side a. Please round to one decimal.

Final Answer:

a =  22.7 ft

Step-by-step explanation:

b=31 ft c=22 ft α=47 ∘  a2 = b2+c2 − 2⋅ b⋅ c⋅ cos α  a=b2+c2−2⋅ b⋅ c⋅ cosα​=b2+c2−2⋅ b⋅ c⋅ cos47° ​=312+222−2⋅ 31⋅ 22⋅ cos47° ​=312+222−2⋅ 31⋅ 22⋅ 0.681998​=22.7=22.7 ft

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The Pythagorean theorem is the base for the right triangle calculator.
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See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

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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