SOLUTION: The ratio of the lengths of the sides of a right triangle is {{{ 1:sqrt (3) :2 }}} . What is the sine of the triangle's smallest angle? Show all steps.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The ratio of the lengths of the sides of a right triangle is {{{ 1:sqrt (3) :2 }}} . What is the sine of the triangle's smallest angle? Show all steps.      Log On


   

Question 1008320: The ratio of the lengths of the sides of a right triangle is +1%3Asqrt+%283%29+%3A2+ . What is the sine of the triangle's smallest angle? Show all steps.
Found 3 solutions by jim_thompson5910, josmiceli, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283%29=1.7 approximately

The legs of this right triangle are 1 and sqrt%283%29. The smaller leg is 1 (since 1+%3C+1.7). The smallest angle will be opposite the smallest leg.

So the opposite side is 1 (in relation to the smallest angle)
The hypotenuse is 2

Sine(smallest angle) = (opposite)/(hypotenuse)
Sine(smallest angle) = 1/2
Sine(smallest angle) = 0.5


Final Answer: 1%2F2 or 0.5

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The smallest angle is opposite the shortest side
The shortest side which is +1+
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The longest side is the hypotenuse
Since +sqrt%283%29+=+1.732+, the longest side is +2+
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If +theta+ is the angle opposite the shortest side,
then +sin%28+theta+%29+=+1%2F2+

Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!

The ratio of the lengths of the sides of a right triangle is +1%3Asqrt+%283%29+%3A2+ . What is the sine of the triangle's smallest angle? Show all steps.
Side ratio-values of: 1%3Asqrt+%283%29%3A2 are consistent with a 30-60-90 special right triangle. In this case, smallest angle is 30%5Eo, and the sine of 30%5Eo is highlight_green%281%2F2%29. 

Verify using the unit circle, or you may know that upon studying trig ratios.