Course Contents Homework31 Applications of Trigonometry H

Course Contents » » Homework31 Applications of Trigonometry » HW31:14 Timer --s evaluate Notes The angle of elevation from a point on the ground to the top of a tree is 38.7 degrees. The angle of elevation from a point 24.5 ft farther back to the top of the tree is 22.1 degrees. Find the height of the tree to 2 decimal places. | height = feet Submit Answer Tries 0/99

Solution

let the height of the tree = h feet

and distance from 1st point to tree = x

tan 38.7= h / x

tan 22.1 = h / ( x + 24.5)

so we can set up the equation

tan 38.7 * x = tan 22.1 ( x + 24.5)

tan 38.7x - tan 22.1 x = 24.5 tan 22.1

x ( tan 38.7 - tan 22.1 ) = 24.5 tan 22.1

x = 25.179929

h = tan 38.7 * 25.179929

h = 20.17

height of the tree = 20.17 feet