A tree 1,900 yards from an observer subtends an angle of 4°. Use the arc length formula to estimate the height of tree.

Question

A tree 1,900 yards from an observer subtends an angle of 4°. Use the arc length formula to estimate the height of tree.

Round the answer to the nearest yard, if necessary.

The height of the tree is approximately   yards.

Answer 1

the circumference of a circle with a radius of 1900 yards would be C = 2 • pi • radius = 2 • pi • 1900 yds, which works out to about 11938 yds.

you want the arc length of 4 degrees out of the entire 360 degrees that make up the circle. multiply the 11938 yds by 4/360 and you get about 132.6 yds.