3 friends are camping in the woods, Bert, Ernie and Elmo. They each havetheir own tent and the tents are set up in a Triangle, Bert and Ernie are 12mapart. The angle formed at Bert is 30°. The angle formed at Elmo is 105°,How far apart are Ernie and Elmo? Round to the nearest one hundredth ofa foot.

If a triangle ABC has angles A, B and C at the points of the named vertices of the triangles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as

[tex]\frac{Sin\text{ A}}{a}=\frac{Sin\text{ B}}{b}=\frac{Sin\text{ C}}{c}[/tex]

For this question,

A = 30°

a = x = ?

B = 105°

b = 12 m

[tex]\begin{gathered} \frac{Sin30\degree}{x}=\frac{Sin105\degree}{12} \\ \frac{0.5}{x}=\frac{0.9659}{12} \\ \text{Cross multiply} \end{gathered}[/tex]

0.9659x = (12) (0.5)

0.9659x = 6

Divide both sides by 0.9659

(0.9659x/0.9659) = (6/0.9659)

x = 6.21 m

But, note that

1 m = 3.281 ft

6.21 m = (6.21) (3.281) = 20.38 ft

Hope this Helps!!!