A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet.
a. Find the length of the side of the lot opposite the 60° angle.
b. Find the length of the hypotenuse of the triangular lot.
c. Find the sine, cosine, and tangent of the 30° angle in the lot. Write your answers as decimals rounded to four decimal places.

Question

A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet.  
 a. Find the length of the side of the lot opposite the 60° angle.         
  b. Find the length of the hypotenuse of the triangular lot.         
  c. Find the sine, cosine, and tangent of the 30° angle in the lot. Write your answers as decimals rounded to four decimal places.

e.mccormick · Answer

Do you know the ratios for a 30-60-90 traingle? http://mathworld.wolfram.com/30-60-90Triangle.html

e.mccormick · Answer

Because the ratios are set, you can find all sides from any one side.

anonymous · Answer

I'm sorry, I'm still confused on how to find the answers @e.mccormick

e.mccormick · Answer

OK.  They give you the side oppoite the 30, right?

e.mccormick · Answer

If we do the ratop as 30:60:90 as in side opposite, then the diagram ratio becomes:

$\dfrac{a}{2}:\dfrac{a\sqrt{3}}{2}:a$

You are given:
$41:x:y$

Now, because you know the first one, it is best... easiest if the ratio you work with has 1 in that spot.  So I am gong to multiply through the first ratio with 2.

$a:a\sqrt{3}:2a$

Ah ha!  Now if you use 41 as a, what do the other two values become?

anonymous · Answer

I'm still quite confused. Sorry math isn't my strong suit... @e.mccormick

e.mccormick · Answer

Replace a with 41 and multiply.

e.mccormick · Answer

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