Solution 4.2:6

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m (Lösning 4.2:6 moved to Solution 4.2:6: Robot: moved page)
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We can work out the length we are looking for by taking the difference
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<center> [[Image:4_2_6.gif]] </center>
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<math>a-b\text{ }</math>
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of the sides
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<math>a</math>
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and
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<math>b</math>
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in the triangles below:
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[[Image:4_2_6_13.gif|center]]
[[Image:4_2_6_13.gif|center]]
[[Image:4_2_6_2.gif|center]]
[[Image:4_2_6_2.gif|center]]
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If we take the tangent of the given angle in each triangle, we easily obtain
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<math>a</math>
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and
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<math>b</math>:
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[[Image:4_2_6_13.gif|center]]
[[Image:4_2_6_13.gif|center]]
[[Image:4_2_6_4.gif|center]]
[[Image:4_2_6_4.gif|center]]
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<math>a=1\centerdot \tan 60^{\circ }=\frac{\sin 60^{\circ }}{\cos 60^{\circ }}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}</math>

Revision as of 08:29, 29 September 2008

We can work out the length we are looking for by taking the difference \displaystyle a-b\text{ } of the sides \displaystyle a and \displaystyle b in the triangles below:

If we take the tangent of the given angle in each triangle, we easily obtain \displaystyle a and \displaystyle b:


\displaystyle a=1\centerdot \tan 60^{\circ }=\frac{\sin 60^{\circ }}{\cos 60^{\circ }}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}

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