Question

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°?

Answer 1

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.

`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

Answer 2

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.