Final answer:
To find the difference between the building and tower heights along with the distance between them, we create two right-angle triangles with angles of elevation and depression. Applying trigonometric functions to the given angles, we can solve for the height difference (x) and the distance using tangent ratios.
Step-by-step explanation:
The question requires the application of trigonometry to solve for the height difference between a building and a tower, and also to find the distance between them, using the given angles of elevation and depression. Since we're given that the building is 60 meters high, with angles of 30° (elevation to the top of the tower) and 60° (depression to the bottom of the tower), we can set up two right-angle triangles to solve for the unknowns.
Using the angle of elevation:
- Let x be the difference in height between the tower and the building.
- The angle of elevation to the top of the tower is 30°.
- Using the formula tan(θ) = opposite/adjacent, we have tan(30°) = x/distance.
Using the angle of depression:
- Let y be the total height of the tower.
- The angle of depression to the bottom of the tower is 60°.
- Using the formula tan(θ) = opposite/adjacent, we have tan(60°) = (60 - y)/distance.
By solving these two equations, we can find x, the difference in height, and the distance between the building and the tower. The difference in height will also give us the height of the tower.