Question

A building lot in a city is shaped as a 30 degrees - 60 degrees - 90 degrees triangle. The side opposite the 30 degree angle measures 41 feet

Answer 1

what are we looking for?

Answer 2

height of building = 41 *sqrt3
im assuming that what u want

Answer 3

Im trying to find the length of the opposite side 60degree angle, what is the length of hypotenuse,and finding sine,cosine, and tangent of the 30 degree angle in the lot in decimals

Answer 4

Let's see...

A 90 * 60 * 30 triangle is actually half of an iscosolece triangle where all the angles and side lengths are the same.

When you cut it in half, you get a 90*60*30 triangle. Now because we know the triangle was originally with all sides equal, we can also know that sin(30) = 1/2 of the hypotenuse if it were 1. This is a trig ratio we know from the unit circle.

The other ratio of the side sin(60) is the square root of three over 2. We get this by using the pythagorean theroem where

\[a^2 + b^2 = c^2\]
In this unit triangle c = 1 and one side = 1/2, so
\[1^2 - 1/2^2 = a^2\]
\[a^2 = \sqrt{3/4}\]
\[a^2 = \sqrt{3}/2\]

If you know that sin(30) = 41, then
\[\sqrt{3}/2*41\]

I hope this helps you figure out the rest of the answers.