SOLUTION: Draw an equilateral triangle and bisect it. Prove that the exact value of the tangent ratios of 30 degree, 45 degree and 60 degree are 0.577, 1,and 1.73, respectively. Please s

Question 206815This question is from textbook Longman Mathematics for IGCSE book 1
: Draw an equilateral triangle and bisect it. Prove that the exact value of the tangent ratios of 30 degree, 45 degree and 60 degree are 0.577, 1,and 1.73, respectively.

Please solve this question. It is from the chapter of trigonometry:Tangent ratios.Thank you very much indeed! This question is from textbook Longman Mathematics for IGCSE book 1

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
DRAW an equilateral triangle. Draw a straight line. Set compass at a convenient distance and keep it there.
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On straight line, mark a starting point. Set compass point in the mark and scribe the line in one spot to indicate the distance. Now from the initial mark strike an arc, about where the vertex might be.
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Move to the other mark on the line and draw an arc to cross the first arc. This should be the vertex.
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to check, set the compass to any side, and check other 2 sides. Allow some error for drafting.
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To bisect, we assume they mean one angle. From both vertex on the original line strike an arc with the compass set at slightly more than midway between. Draw a straight line between the arc intersections. This should be a perpendicular bisector of the base, and should pass thru the top vertex.
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If they want you to bisect all of the angles, repeat for the other angles.
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For the second problem, Draw a right triangle.
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For 30 degrees, mark one of the leg angles 30. The other leg is the 90 degree angle. Either using the trig tables, or remembering the info for standard triangles, we know that the hypotenuse(side opposite right angle) is = 2,,,the side opposite the 30 deg angle is = 1, and the other side is = sqrt 3.
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The tan of 30 is opposite side / adjacent side, or 1/sqrt 3 = .577
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For 60 degrees, use the same picture. The odd angle is 60 degrees. (the one not 30 or 90).
The tan of 60 = sqrt3 / 1= 1.732
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for 45 degrees, we need a new sketch. Again a rt triangle, sides labeled 1, 1, and sqrt2,(with sqrt2 being the hypotenuse)
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The tan of 45, is again opposite /adjacent, or 1/1= 1
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Hopefully this helps
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keep up the good work

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