Two points lie on opposite sides of a tower, on a line through its foot, 105 m apart…

Step 1. The distances. The point with $30°$ is $h\cot 30° = h\sqrt{3}$ from the foot. The point with $45°$ is $h\cot 45° = h$ from the foot.

Step 2. They add to $105$ m. $h\sqrt{3} + h = 105$, so $h(\sqrt{3} + 1) = 105$.

Step 3. The height. $h = \dfrac{105}{2.732} \approx 38.43$ m.

Step 4. The larger distance. $38.43 \times 1.732 = 66.57$ m.