Math, Trigonometry

Question

Molly and James are on the opposite sides of a river. To find the width of the river, each of them hammers a stake on his/her bank of the river on such a way that the distance between the two stakes approximates the width of the river. Molly walks 10 ft away from her stake along the river and finds that the line of sight from her new position to her stake from 73deg34' angle. How wide is the river?

Answer 1

I hope I am reading the question correct. I wrote this out on paper but I see no way to submit an image.

Angle (theta) = 73 + (34/60) degrees

Opposite Side from Angle (theta) = approximate width of the river = o

Adjacent Side from Angle (theta) = Molly's Walking distance = a

soh cah toa

We have o and a so only t is missing. Use toa

t=o/a

tan(theta)= o/a

We have a value for angle theta and a value for a. We must get them in the same side so we can solve for o. Multiply a to both sides. It cancles out on the right side of the equation.

(a)tan(theta)=o

Plug in our known values

(10)tan(73 +34/60)=o

Make sure you calculator is in degrees.

33.9 ft = o

The approximate width of the river is 33.9 ft.

Answer 2

73°+34/60º=73.566667 º

tan(73.566667)=w/10

w=33.9 ft