A tree on one side of a river is due west of a rock on the o

A tree on one side of a river is due west of a rock on the other side of the river. From a stake 26.0 yards north of the rock, the bearing of the tree is S 19.2 degree W. How far is it from the rock to the tree rounded to the nearest tenth of a yard?

Solution

Ok, first draw a triangle. The tree is due west of the rock, so it is straight left of the rock. The stake is 26 yards North, which is straight up. So your triangle should have a 90 degree angle between the line from tree to rock and the line from rock to stake.
Label the line between the tree and the rock as X.

Then the problem tells you the angle from the stake to the tree is 19.2 degrees. Looking at your triangle, use a trig identity. The

tan 19.2 degrees = X/26(opposite side over adjacent).

multiply both sides of the equation by 26. So you have 26tan(19.2) = X

X=26 (0.348236) = 9.05 yards.

, X=9.05 yards