Two office towers are 43m apart. From the top of the shorter tower, the angle of elevation to the top of the taller tower is 26o while the angle of depression to the base is 51o. Determine the height of each tower and round your answers to one decimal place.

To solve this problem, we can use trigonometry. Let's assign labels to the information given:

- Let A be the top of the taller tower.
- Let B be the top of the shorter tower.
- Let C be the base of the taller tower.

To find the height of each tower, we can use the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

1. Find the height of the taller tower (AC):
- We have the angle of elevation from B to A, which is 26 degrees.
- Using the tangent function: tan(26) = AC / 43
- Rearranging the equation: AC = 43 * tan(26)
- Calculate: AC ≈ 19.8 meters (rounded to one decimal place)

2. Find the height of the shorter tower (BC):
- We have the angle of depression from B to C, which is 51 degrees.
- Using the tangent function: tan(51) = BC / 43
- Rearranging the equation: BC = 43 * tan(51)
- Calculate: BC ≈ 53.7 meters (rounded to one decimal place)

Therefore, the height of the taller tower is approximately 19.8 meters and the height of the shorter tower is approximately 53.7 meters.