Find the measure of each angle to the nearest tenth of a degree. cosine= Y 0.5135
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Go to http://mathworld.wolfram.com/Cosine.html
432229
first draw a circle, and then put the star in it w/ the points touching the edge. that divides the circumference of the circle into 5 equal parts. so to find the degree of each one of those section divide 360 by 5 = 72. now look at the angle that is made from the lines from the ends of the individuals sections to the point of the star it goes to, which is the inscribed angle. now that angle which is one of the acute angles is half of its intercepted arc. so that makes 72 divided by 2= 36. so since you wanted to know the measure of all the acute angles and not just one multiply 36 times 5 = 180
634140
Brian gave you the answer, but he didn't explain it thoroughly.\n\nPlace your vector at the origin of an x and y plane.  The x and y axes are perpendicular, so you can use the Pythagorean formula to get the magnitude which is the length of the hypotenuse of the right triangle formed by the points (0,0), (10,0), and (0,8). sqrt(10^2+8^2)\n\nNow you need direction which is the angle between the x axis and the vector. Since you have solved for all three lengths of the triangles sides, you can use any inverse trig function to find the angle.  Brian chose tangent.\n\nGood work, Brian!
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I think that what you really want here is the tangent ratio. You know the slope of the line, right (hint, it is right there in the equation)? You know that the tangent ratio is a over b (where a and b are the non-hypotenuse sides of the triangle), right? You should be able to use that to figure out the tangent of the angle made by the line. Now all you have to do is figure out the angle that has that number as a tangent. That would be the "tan -1" (inverse tangent) function on your calculator.\n\nIf you are working from trig tables rather than a calculator, find the number in the second column of the tangent table that is closest to your tangent number then look in the first column for the angle.\n\nIf you are required to use sin and cosine remember your Pythagorean theorem and use it to find the hypotenuse.\n\nASIDE TO Drakestone: Your solution only finds the sine of the angle, not the angle itself. You need to apply "sin -1" to your answer to get the final answer.\n\n\nASIDE TO eternal...: You are wrong too. graph y=5x+3 and you will see that it is way too steep to be an 11 degree angle. You mixed up your opposite and adjacent values in calculating your tangent.
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You're looking for the angle that has a sine of 1/2.\nDrawing a triangle representing this is very helpful.  You will see that it is a 30-60-90 triangle.  \nIf you can find it in degrees, then you can convert it to radians by multiplying it by pi/180.\nsine(30) = 1/2\n30 degrees = 30(pi/180) = pi/6
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The probability would be zero.  Since the angles of a triangle in this case would be considered a continuous random variable (meaning that the angle could be anything in the range of (0, 180)), the probability that you would find a triangle with an angle that is exactly 45 degrees is impossible.\n\nThis is analogous to finding a person who is exactly 6 feet tall.  You may find a person who is close to being 6 feet tall, but their height will always be off by a fraction of an inch.  Same is true with the triangles; you may be able to find a triangle that has an angle very close to 45 degrees, but that angle will always be off by a fraction of a degree.
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1. Find x to the nearest length\nWhat would x be if it is a right triangle with the cos angle at 32º,sin angle at 58º and a hypotenuse length at 10\n\ncos 32 = x/10\n\nSo x = 8.48\n\n2.Find the missing side lengths for x and y.\nthe triangle is a 30-60-90 and it has a hypotenuse of 8. the sin leg is x and the cos leg is y\n\nsin30=x/8\nx = 4\n\ncos30 = y/8\ny = 4√3\n\n3. a ladder 18 feet long makes an angle of 61º with the ground as it leans against a barn. How far up the side of the barn does the ladder reach?\n\nThe ladder leaning against the barn makes a right-angled triangle with a hypotenuse of 18.\n\nLet x be the height of the triangle. Then:\n\nsin61 = x/18\nx = 15.74 feet\n\n4. also, to make sure i did things correctly, is the Sec36º -.128? and is the cot60º the squareroot of 3 /3?\n\nNo, that is incorrect.\n\nsec 36 = 1/cos36 = 1.236\n\ncot60 = cos60/sin60 = (1/2)/(√3/2) = 1/√3\n\n5. Is sec 30º =2? \n\nsec30 = 1/cos30 = 1/sin30 = 2
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y = 11.03 and x = 4.23\n\n10/y = cos(25) = 0.906; so y = 10/0.906 = 11.03\n\nx/y = sin(25) = 0.423; so x = 10x0.423 = 4.23
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I wanted to give a partial answer that wasn't presented elsewhere:\n\ne.g. Sine 10 deg =0.174, while cosine 80 deg= 0.174. how ironic is that?!!\n\nIt's not ironic at all.  If you have a right triangle, you know one angle is 90°, and the sum of all angles must be 180°, so the other two angles must add to 90.  You give sin 10°, so the other angle must be 80°.\nThe sin of any angle must be equal to the cos of its complementary angle (x and 90°-x are complementary), because of the definitions.  The side opposite the x angle is adjacent to the the 90°-x angle.\nThus sin 10° = cos 80°.
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cos^-1(0.5)=pi/3\ntan pi/3=rt3
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The only possible answer for your fixed number would be zero.  So you just have to do some inverse trig functions to get the value for x.  \n\nSolved:\nLet x=1.0038848219 [radians]\nTan(1.0038848219)=1.570796327=pi/2\nCos(pi/2)=0\nSin(0)=0
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Since the radius is 44, you could go either 44 units left, right, up or down from the center and find a point on the circle itself.  So (44,0) would be one such point.  However, these points are not in a quadrant; they are on an axis.  All the other points would fit in the circle's equation, x^2 + y^2 = 44^2.  So pick a number for the x-coordinate, square it, subtract this from 44 squared, then do the square root.  That gives you the y-coordinate.
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cos(315)degrees=cos(360-45degrees)\n               =cos 45degrees\n               =1/root2
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angleB=angleC=(180-22)/2\n=158/2=79* apiece
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just put in the exact values for the unit circle sin(30) is 1/2, cos(30) is square root 3/2, cot(30) is cos(30)/sin(30) and csc(30) is 2.
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a) Assume the following:\n\nAngles a= 10 deg, b= 80 Deg, c=90 deg \nHypotenuse length = 2.5 m\nheight = 2.5 * cos 80 Deg= .434 m\nlength = 2.5 * sin 80 Deg= 2.462 m\nacceleration = "g" * Sin 10 Degree
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Draw a right angled triangle.  the vertical is 35m and the sloped line, the hypotenuse, is 50m.  We have to find the angle between the string and the ground.\n\n35 is the opposite, 50 is the hyp, so it is a sine problem.  Sin x = opp/hyp = 35/50.\n\nusing the inverse sine function on the calculator, we find that the angle is 44.4 degrees\n\nhope this helps