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°?

2 Answers
May 2, 2017

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.

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#c^2=a^2+b^2# in this case.

and #sin(alpha)=a/2# which #alpha# has a value of 30 degrees and we know that #sin(30)=0.5#

Now you can write down if c=1,

#1=0.5^2+0.866^2#

You can also visit other explanations such as:

http://mathworld.wolfram.com/30-60-90Triangle.html

May 2, 2017

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"#

#"Use of Pythagoras gives the third side of length " sqrt3#

#"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.