To solve this problem, let's start by labeling the sides of the triangle formed by the cable and the buildings.
Let's call the height of the taller building 'x'. The shorter building is given as 12.0 m.
Now, let's label the other sides of the triangle. The cable is given as 23.5 m. We'll call the horizontal distance between the two buildings 'd'.
To find the height of the taller building, we need to use trigonometry. Since we have the angle and the opposite side, we can use the tangent function.
The tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the taller building (x), and the adjacent side is the horizontal distance between the buildings (d).
The formula for the tangent function is:
tan(theta) = opposite / adjacent
In this case, we have:
tan(13 degrees) = x / d
Now, to find the height of the taller building (x), we need to solve for x.
Rearranging the equation, we have:
x = tan(13 degrees) * d
To find the value of d, we can use the Pythagorean theorem:
d^2 = 23.5^2 - 12^2
Simplifying this equation, we have:
d^2 = 551.75 - 144
d^2 = 407.75
Now, we can find the square root of both sides to find the value of d:
d â â407.75
Using a calculator, we find that d â 20.1943
Now, substituting the value of d back into our equation for x, we have:
x = tan(13 degrees) * 20.1943
Calculating this using a calculator, we find that x â 4.8
Therefore, the height of the taller building to the nearest tenth of a meter is approximately 4.8 meters.