Question

A camper wants to know the width of a river. From point A, he walks downstream 60 feet to point B and sights a canoe across the river. It is determined that $\alpha$ = 34°. About how wide is the river?
A. 34 feet
B. 50 feet
C. 89 feet
D. 40 feet

Answer 1

Hello!

The answer is:

The correct option is:

D. 40 feet.

Why?

To solve the problem and calculate the width of the river, we need to assume that the distance from A to B and the angle formed between that distance and the distance from A to the other point (C) is equal to 90°, meaning that we are working with a right triangle, also, we need to use the given angle which is equal to 34°. So, to solve the problem we can use the following trigonometric relation:

$Tan\alpha =\frac{Opposite}{Adjacent}$

Where,

alpha is the given angle, 34°

Adjacent is the distance from A to B, which is equal to 60 feet.

Opposite is the distance from A to C which is also equal to the width of the river.

So, substituting and calculating we have:

$Tan(34\°) =\frac{Width}{60ft}$

$Width=60ft*Tan(34\°)=60ft*0.67=40.2ft=40ft$

Hence, we have that the correct option is:

D. 40 feet.

Have a nice day!

Answer 2

Answer: OPTION D

Step-by-tep explanation:

Observe the figure attached.

You can notice that the the width of the river is represented with "x".

To calculate it you need to use this identity:

$tan\alpha=\frac{opposite}{adjacent}$

In this case:

$\alpha=34\°\\opposite=x\\adjacent=60$

Now you must substitute values:

 $tan(34\°)=\frac{x}{60}$

And solve for "x":

$60*tan(34\°)=x\\\\x=40.4ft$

$x$≈$40ft$