Question

Explain how to use the measures of a right triangle to calculate the exact value of sin 30 degrees? How can this information be used to determine the exact value of sine 60 degrees?

Answer 1

@Hero @Luis_Rivera @experimentX @robtobey @phi @Preetha @hartnn @hba @kropot72 @nubeer

Answer 2

@.Sam. @waterineyes

Answer 3

@jhonyy9 @lalaly @cwrw238 @ganeshie8

Answer 4

@phi

Answer 5

How does this answer my question?

Answer 6

This question is a bit fuzzy. The standard derivation for showing that the sin 30º= 0.5
is to start with an equilateral triangle with 3 sides = a, and 3 angles=60º

construct the angle bisector of one of the angles (see luis picture). this will form two congruent triangles by angle-side-angle (30 by construction, side=a, angle=60)
the 3rd angle in both triangles =90 because the 3 angles must add to 180:30+60+90=180

at this point we know the side opposite the 30º is a/2 (because the two triangles are congruent, and together their short sides make up a full side = a of the equilateral triangle)

now we can use the definition of sin to show sin(30)= \(\frac{ \frac{a}{2}}{a} = \frac{1}{2}\)

Answer 7

How does a/2/a equal 1/2? @phi

Answer 8

one way to show it is multiply top and bottom by 1/a
\[ \frac{ \frac{a}{2} \cdot \frac{1}{a}}{ a\cdot \frac{1}{a}} \]
the bottom a*1/a is 1 and you have
\[ \frac{ \frac{a}{2} \cdot \frac{1}{a}}{1} =\frac{\cancel{a}}{2} \cdot \frac{1}{\cancel{a}} = \frac{1}{2}\]

Answer 9

Ok, thanks, how about for sin 60 degrees in the question?

Answer 10

use pythagoras to find the other leg. sin(60)= other leg/ hypotenuse

Answer 11

The question asks how the information can be used to determine the exact value of sin 60, im kind of confused how I answer this?

Answer 12

once you know the hypotenuse is a, the side opposite 30º is a/2 you can find the side opposite 60º using pythagoras: a^2+b^2=c^2

Answer 13

Thank you so much :)