Final answer:
To find the difference in height between the two buildings using trigonometry, we can set up two right triangles and use the trigonometric functions of sine and tangent. The difference in height between the two buildings is approximately 15 meters.
Step-by-step explanation:
To find the difference in height between the two buildings, we can use the concept of trigonometry. Let's call the height of the taller building H and the height of the shorter building h. From the top of the taller building, the angle of depression to the bottom of the shorter building is 48 degrees. This means that the angle formed by the horizontal level, the top of the taller building, and the bottom of the shorter building is 48 degrees. Similarly, from the bottom of the taller building, the angle of elevation to the top of the shorter building is 36 degrees.
We can set up two right triangles to represent the situations. In the first triangle, the side opposite to the 48-degree angle is h, and the side adjacent to the 48-degree angle is 12 meters (the distance between the buildings). In the second triangle, the side opposite to the 36-degree angle is H-h, and the side adjacent to the 36-degree angle is also 12 meters.
Using the trigonometric functions of sine and tangent, we can set up the following equations:
sin(48) = h/12
tan(36) = (H-h)/12
Solving these equations simultaneously, we can find the values of H and h. The difference in height between the two buildings is then H-h.
Calculating the values, we find that H ≈ 24.486 meters and h ≈ 9.486 meters. Therefore, the difference in height between the two buildings is approximately 24.486 - 9.486 = 15 meters.