Question

A surveyor measures the distance across a straight river by the following method:starting directly across from a tree on the opposite bank, he walks x=102m along the riverbank to establish a baseline. Then he sights across to the tree. The angle form his baseline to the tree is theta=39.8 degrees. How wide is the river ?

Answer 1

Let $A$ be the point of tree's location (see the figure). Then we need to find side $AB$ from the right triangle $\triangle ABC$. By definition of tan function, obtain:

$$AB = x\tan \theta$$

Substituting $x = 102 m, \theta = 39.8\degree$, obtain:

$$AB = 102\cdot \tan39.8\degree \approx 85m$$

Answer. 85 m.