Question

An engineer needs to determine the distance across a river without swimming to the other side. The engineer notices a tree on the other side of the river and suddenly has an idea.

Describe how she will sketch her idea to be able to determine the distance. Make a sketch and support you figure by number use meter as unit.

Answer 1

Explanation:

The engineer can use a clinometer to measure the angle of elevation of the top of the tree. Let the height of the tree be represented by x, the she could determine the distance across the river, d, by applying the trigonometric function.

Tan θ =
`(opposite)/(adjacent)`

=
`(x)/(d)`

the the distance, d = x ÷ Tan θ

Assume the angle of elevation of the top of the tree is
`30^(o)`, and the height of the tree is 10 m, then the distance, d, across the river would be;

d =
`(10)/(0.5774)`

= 17.3190

d = 17.32 m

The sketch to the explanation is attached to this answer for more clarification.