Find the greatest number by which 90, 120 and 150 are exactly divisible.
2 answers:
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The angle is 127°, so the Pythagorean theorem does not apply.
Generally, you would use the Law of Cosines to solve for the third side when given two sides and the angle between them.
EF^2 = 7^2 +15^2 -2*7*15*cos(127°)
EF ≈ √(400.3812) ≈ 20.00953
My guess is that you're expected to use 20 for the length of the 3rd side.
By Heron's formula, s = (7 +15 +20)/2 = 21
Area = √(21*(21 -7)*(21 -15)*(21 -20)) = √(21*14*6*1) = √1764 = 42 . . . . yd^2
_____
More directly,
.. Area = (1/2)*7*15*sin(127°) ≈ 41.928 . . . . yd^2
Generally, you would use the Law of Cosines to solve for the third side when given two sides and the angle between them.
EF^2 = 7^2 +15^2 -2*7*15*cos(127°)
EF ≈ √(400.3812) ≈ 20.00953
My guess is that you're expected to use 20 for the length of the 3rd side.
By Heron's formula, s = (7 +15 +20)/2 = 21
Area = √(21*(21 -7)*(21 -15)*(21 -20)) = √(21*14*6*1) = √1764 = 42 . . . . yd^2
_____
More directly,
.. Area = (1/2)*7*15*sin(127°) ≈ 41.928 . . . . yd^2
