Question

section 1.2 modeling and alternative representations

1. a surveyor measures the distance across a straight river by the following method (fig. p1.6). starting directly across from a tree on the opposite bank, she walks ( d = 100 ) m along the riverbank to establish a baseline. then she sights across to the tree. the angle from her baseline to the tree is ( \theta = 35.0^circ ). how wide is the river?

figure p1.6

Explanation:

Step1: Define variables and trigonometric relation

Let $w$ = river width. Use tangent: $\tan\theta = \frac{w}{d}$

Step2: Rearrange to solve for $w$

$w = d \times \tan\theta$

Step3: Substitute given values

$w = 100 \times \tan(35.0^\circ)$
$\tan(35.0^\circ) \approx 0.7002$, so $w \approx 100 \times 0.7002$

Answer:

The width of the river is approximately 70.0 meters.