1 4 points A tree on one side of a river is 32 ft due north

1. (4 points) A tree on one side of a river is 32 ft due north of a rock on the other side of the river From a stake west of the rock, the bearing of the tree is N 75° E. a. How far is it from the rock to the stake? b. How far is it from the tree to the stake?

Solution

the rock makes a right angled triangle

let distance from rock to stake = xft

tan 75 = 32 / x

x = 32 / tan 75

x = 8.5743 feet

b) let distance from stake to tree is h

sin 75 = 32 / h

h = 32 / sin 75

h = 33.13 feet