How do I solve a height and distance problem with an angle of elevation of 30°?

First draw the figure: the tower is vertical, the point is on the ground, and the angle of elevation is the angle at the ground point looking up to the top. Label the tower height as h and the horizontal distance as 30 m. From the observer, the height is the opposite side and the distance is the adjacent side, so you use tan because tan = opposite/adjacent. So tan 30° = h/30. Since tan 30° = 1/√3, we get 1/√3 = h/30, giving h = 30/√3 = 10√3 m, which is about 17.32 m. The key skill is identifying which sides are opposite and adjacent to the given angle, then picking the ratio that connects them.