A person standing 50 feet from the base of a tower observes the top of the tower at an angle of elevation of 40°. To the nearest tenth of…

The tower, the ground, and the line of sight form a right triangle. The angle of elevation is $40°$, the adjacent side is 50 feet, and the opposite side is the height. Tangent connects them: $\tan(40°) = \frac{h}{50}$, so $h = 50 \times 0.839 = 41.95$, which rounds to 42.0 feet. A common wrong answer is 38.3, which comes from using sine or cosine incorrectly (such as $50 \cos 40° \approx 38.3$). Another is 59.6, from dividing $\frac{50}{0.839}$, which inverts the relationship. Choose the ratio that links opposite and adjacent.