In a 30-60-90 triangle, there is a known ratio of the sides.

If the angles are 30:60:90, then the sides across from the respective angles are 1:sqrt(3):2.

So if the side across from the 30 degree angle is 41 feet, we can set up something to cross-multiply:

(a)

Using the ratio to find the side across from the 60 degree angle:

1/41feet = sqrt(3)/x

---------cross multiply --------

x = 41* sqrt(3) feet

-------- calculate ----------

x = 71.01 feet

(b)

Using the ratio to find the side across from the 90 degree angle (hypotenuse):

1/41feet = 2/x

---------cross multiply --------

x = 41* 2 feet

-------- calculate ----------

x = 82 feet

(c)

Have you learned SOHCAHTOA?

this means:

Sine equals

Opposite over

Hypotenuse,

Cosine equals

Adjacent over

Hypotenuse,

Tangent equals

Opposite over

Adjacent

sine30 = opposite/hypotenuse = 41/82 = 1/2 = 0.5

cosine30 = adjacent/hypotenuse = 71.01/82 = 0.866

tangent30 = opposite/adjacent = 71.01/41 = 1.73

where is this small building