Find the remaining sides of a 30° — 60° — 90° triangle if the side opposite 60° is 42.

Question

Find the longest and the shortest side

Answer 1

 

Using the triangle we see that to find x we need to use the tangent function

tan 30 = x/42

x = 42tan 30

x = 24

to find the hypotenuse we use pythagorean thereom

24^2 + 42^2 = H^2

576 + 1764 = H^2

H^2 = 2340

H = |48|

length cannot be negative.

Therefore the sides are 42, 24, and 48

Answer 2

 

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.