During the afternoon, an 18-foot tall tree casts a shadow 25 feet long. What is the approximate angle of elevation from the end of the shadow to the top of the tree with respect
to the ground?

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

The triangles in the diagram are congruent. if mzf = 40°, mza = 80°, and mzg = 60°, what is mzb?

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =