From two points each on the opposite sides of a river,the angles of elevations of the top of an 80ft. tree are 60 degree & 30 degree.the points & the tree are in the same straight line,which is perpendicular to the river.how wide is the river?

Answer 1

First, we draw a ver line which represents the tree and label it 80ft.
Then we draw a hor line to the base of
the tree. The other end of the hor line goes to the top of the tree and represents the hyp of a rt triangle.

Draw a 2nd hyp from the top of the tree
to a point on the hor line about 1/3 of
the distance to the bottom of the tree.
Label the segment between the 2 hyps
X1 and the segment connecting to the
bottom of the tree is X2.

The angle between the longest hyp and
hor line is 30 deg and the angle formed
by the shortest hyp is 60 deg.

tan30 = Y/(X1 + X2) = 80 / (X1 + X2),
X1 + X2 = 80 / tan30 = 138.6ft.

X2 = 80 / tan60 = 46.2ft.

X1 + X2 = 138.6,
X1 + 46.2 = 138.6,
X1 = 138.6 - 46.2 = 92.4ft. = Width of
the river.