Can someone please help me explain how to use the measures of a right triangle to calculate the exact value of sin 30°?
How can this information be used to determine the exact value of sin 60°?
How can this information be used to determine the exact value of sin 60°?
2 Answers
Triangle.
Explanation:
If you have a right triangle, you have distances like a (for your far neighbour), b (for your near neighbour) and c (hypotenuse) in your triangle.
and
Now you can write down if c=1,
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see explanation.
Explanation:
Apologies for not having diagrams in this explanation.
#"Beginning with an equilateral triangle of side 2 units and"#
#"3 angles of size "60^@#
#" Draw an altitude from one of the vertices of the triangle"#
#"We obtain 2 triangles but need only consider one"#
#"This is a right triangle with angles of " 60^@" and " 30^@#
#"The hypotenuse is 2, the base is 1"#
#"Hence we have a right triangle with angles " #
#90^@-60^@-30^@" and sides " 1-2-sqrt3#
#"from this triangle we can obtain the trig. ratios"#
#"for sin / cos and tan as exact values"#
#rArrsin30^@=1/2" and " sin60^@=sqrt3/2# This triangle is well documented and should be found in any math text or on the internet.