An observer stands 50 feet from the base of a tower. The angle of elevation to the top of the tower is 38°. Which value is closest to the…

The tower, the ground, and the line of sight form a right triangle. The height is opposite the $38^\circ$ angle and the $50$ feet is adjacent, so use the tangent: height $=50\tan38^\circ\approx50(0.781)\approx39$ feet, choice B. Choice C ($63$) is $\frac{50}{\cos38^\circ}$, the length of the line of sight, which is the hypotenuse rather than the height. Choice A ($31$) is $50\sin38^\circ$, which uses sine as if $50$ were the hypotenuse. Choice D ($79$) is not produced by a trigonometric ratio that matches the figure. With an angle under $45^\circ$, the height must be less than the base distance of $50$.