How wide is the river?

Question

Mai Khanh wants to measure the width of a river. She stretchesa 100-yard string parallel to the river along the ground. (The river is completely straight for these 100 yards.) Directly across the river from one end of the string is a tree on the riverbank. From the other end of the string, she sights to the tree and finds that the angle between the string and the line of sight to the tree is 35 degrees. What is the approximate width of the river?

Please show all steps!

Thank you!

Answer 1

You have a right triangle:
(a) the string,
(b) the line perpendicular to the string straight across the river from one end of the string to the tree, and
(c) the line of sight from the other end of the string to the tree (which is the hypotenuse of the right triangle)

From the 35-degree angle, the opposite leg is the width of the river, and the adjacent leg is the string.

tan(x) = opposite/adjacent
tan(35) = width/100yd
100yd * tan(35) = width
100yd * 0.70020754

width = about 70 yards

Answer 2

Draw a right angled triangle ABC
Right angle at B
BC is string.
A is tree
Angle ACB = 35°
tan 35° = AB / 100
AB = 100.tan 35°
AB = 70 yds ( to nearest whole number)
Width of river = 70 yds.