A tree grows vertically on a slope which has an incline of 27 degrees. When the sun is at an elevation of 78 degrees, the tree casts a shadow of 48 feet directly down the slope.

Answer 1

sketch a line making an angle of 27° with the horizontal.
Label the length of the tree's shadow on that line as AB, with B the foot of the tree.
Let the top of the tree be C
(so we need BC)

from A draw a horizontal and let CB extended hit that horizontal at D
in the right-angle triangle , angle BAD = 27° so
angle ABD = 63°, making angle ABC = 117°

So in triangle ABC,
AB = 48
angle ABC = 117°,
angle CAB = 78-27 = 51°
making angle ACB = 12°

by the sine law:
BC/sin51 = 48/sin12
BC = 48sin51/sin12

carry on