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Writing x instead of theta, cos2x = 1 - (12/13)2 = 1 - 144/169 = 25/169 = (5/13)2 So cos(x) = ± 5/13 so that x = cos-1(5/13) or cos-1(-5/13) And then, depending on the range of x, you have solutions for x. A calculator will only give you the principal solutions, though.
a = 3/sqrt(2)*i + 3/sqrt(2)*jb = 5ja.b = |a|*|b|*cos(q)= 3*5*cos(45) = 15/sqrt(2)
To find the hypotenuse with angle a and side b, we use the identity below:cos(a) = b/cWe have a and b, and to find c, we multiply both sides by c and divide both sides by cos(a):c = b/cos(a)c = 5/cos(30)c = 32.41460617mm
5/13 = 0.3846 (to 4 dp)
Why approximate? I will show you what you should know being in the trig section. Law of cosines. Degree mode!! a = 4 (angle opposite = alpha) b = 5 ( angle opposite = beta) c = 8 ( angle opposite = gamma ) a^2 = b^2 + c^2 - 2bc cos(alpha) 4^2 = 5^2 + 8^2 - 2(5)(8) cos(alpha) 16 = 89 - 80 cos(alpha) -73 = -80 cos(alpha) 0.9125 = cos(alpha) arcos(0.9125) = alpha alpha = 24.15 degrees ------------------------------ b^2 = a^2 + c^2 - 2bc cos(beta) 5^2 = 4^2 + 8^2 - 2(4)(8) cos(beta) 25 = 80 - 64 cos(beta) -55 = -64 cos(beta) 0.859375 = cos(beta) arcos(0.859375) = beta beta = 30.75 degrees --------------------------------- Now to find gamma, subtract from 180 degrees 180 - 24.15 - 30.75 = 125.1 degrees alpha = 24.15 degrees ( subject to rounding, but all add to 180 degrees ) beta = 30.75 degrees gamma = 125.1 degrees now you see the smallest, the angle opposite the a side, which is 4 ( be in degree mode!!)
It is: cos^-1(12/13) = 22.61986495 degrees
The answer depends on which of the three angles 'a' is!
It is: cos = adj/hyp and the acute angles for the given right angle triangle are 67.38 degrees and 22.62 degrees
It is about 67 degrees
4/5
Writing x instead of theta, cos2x = 1 - (12/13)2 = 1 - 144/169 = 25/169 = (5/13)2 So cos(x) = ± 5/13 so that x = cos-1(5/13) or cos-1(-5/13) And then, depending on the range of x, you have solutions for x. A calculator will only give you the principal solutions, though.
a = 3/sqrt(2)*i + 3/sqrt(2)*jb = 5ja.b = |a|*|b|*cos(q)= 3*5*cos(45) = 15/sqrt(2)
To find the hypotenuse with angle a and side b, we use the identity below:cos(a) = b/cWe have a and b, and to find c, we multiply both sides by c and divide both sides by cos(a):c = b/cos(a)c = 5/cos(30)c = 32.41460617mm
The answer is 13. x=13 13*5+13*2=91 Thank you.
5/13 = 0.3846 (to 4 dp)
Why approximate? I will show you what you should know being in the trig section. Law of cosines. Degree mode!! a = 4 (angle opposite = alpha) b = 5 ( angle opposite = beta) c = 8 ( angle opposite = gamma ) a^2 = b^2 + c^2 - 2bc cos(alpha) 4^2 = 5^2 + 8^2 - 2(5)(8) cos(alpha) 16 = 89 - 80 cos(alpha) -73 = -80 cos(alpha) 0.9125 = cos(alpha) arcos(0.9125) = alpha alpha = 24.15 degrees ------------------------------ b^2 = a^2 + c^2 - 2bc cos(beta) 5^2 = 4^2 + 8^2 - 2(4)(8) cos(beta) 25 = 80 - 64 cos(beta) -55 = -64 cos(beta) 0.859375 = cos(beta) arcos(0.859375) = beta beta = 30.75 degrees --------------------------------- Now to find gamma, subtract from 180 degrees 180 - 24.15 - 30.75 = 125.1 degrees alpha = 24.15 degrees ( subject to rounding, but all add to 180 degrees ) beta = 30.75 degrees gamma = 125.1 degrees now you see the smallest, the angle opposite the a side, which is 4 ( be in degree mode!!)
The angle of Q works out as: cos-1((6*square root of 5)/15) = 26.6 degrees to 1 decimal place