Asked by Meghan
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.
Answers
Answered by
Reiny
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
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
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