Question

Using a transit, a surveyor measures the angle between two trees to be 111 degrees. If the first tree is 62 feet from the transit and the second tree is 58 feet from the transit, what is the distance between the two trees? ​

Answer 1

The distance between the two trees is
`98.92\ ft`

Explanation:

we know that

Applying the law of cosines

`c^(2)=a^(2) +b^(2) -2(a)(b)cos (C)`

where

c -----> is the distance between the two trees

a ----> is the distance between the transit and the first tree

b ----> is the distance between the transit and the second tree

we have

`a=62\ ft`

`b=58\ ft`

`C=111\°`

substitute and solve for c

`c^(2)=62^(2) +58^(2) -2(62)(58)cos (111\°)`

`c^(2)=9,785.38`

`c=98.92\ ft`