Question

A biologist wants to know the width w of a river in order to properly set instruments for studying the pollutants in the water. From point A, the biologist walks upstream 100 feet and sights to point C. From this sighting, it is determined that θ = 56° (see figure). How wide is the river? Verify your result numerically. (Round your answer to one decimal place.)

Answer 1

Answer:   The river is 148.3 feet wide.

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

The triangle formed is a right triangle.

Using SOH CAH TOA

$tan 56 = \frac{x}{100}$

Multiplying 100 in both sides

$x = 100 \times tan56$

$x = 100 \times 1.4826$

$x = 148.26$

Rounding to the one decimal place

$x = 148.3$

Hence river is 148.3 feet wide.   .............. Answer

Hope it will help :)

Answer 2

The required wide w of the river is 148.3 feet.

Given that,

Point A, the biologist walks upstream 100 feet and sights to point C.

From this sighting, it is determined that θ = 56° .

We have to determine,

How wide is the river.

According to the question,

This forms a right angled triangle with the adjacent side to the 56degrees angle and the opposite side = width of the river.

So,  tan56 = opposite side / adjacent side.

Therefore,

$tan56 = \frac{x}{100}$

Where x = the width of the river.

$x = 100\times tan56\\\\x = 100\times1.48\\\\x = 148.3$

Hence, The required wide w of the river is 148.3 feet.

For the more information about Trigonometry click the link given below.

https://brainly.com/question/4380869