Question

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.

Answer 1

Ernie and Elmo are 20.38 ft. apart

Step-by-step explanation

To answer this question, we need to first sketch the triangle for this scenario

Let the distance between Ernie and Elmo be x

The Sine rule is used to solve angles and sides of triangle.

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

`\frac{Sin\text{ A}}{a}=\frac{Sin\text{ B}}{b}=\frac{Sin\text{ C}}{c}`

For this question,

A = 30°

a = x = ?

B = 105°

b = 12 m

`\begin{gathered} (Sin30\degree)/(x)=(Sin105\degree)/(12) \\ (0.5)/(x)=(0.9659)/(12) \\ \text{Cross multiply} \end{gathered}`

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!!!