Solving the Problem with Sloping Lines
First, let's define the symbols. TC is the first sloping line, while TD is the second sloping line. Let the point T be the point where the two lines meet. Furthermore, let the symbol φ represent the plane where the projections of TC and TD are measured. Finally, TP and DP represent the projections of TC and TD, respectively.
Now, we can use the given information to write equations. The sum of the two slopes, TC and TD, is equal to 10 cm. This can be written as:
TC + TD = 10 cm
We also know that the projection of TC on plane φ, TP, is equal to 6 cm. Similarly, the projection of TD on plane φ, DP, is also equal to 6 cm. We can express this as the following equations:
TP = 6 cm
DP = 6 cm
Now, we can use the Pythagorean theorem to find the length of TC and TD. Since the length of TC on plane φ is equal to 6 cm, we can use TP and TD to find it. The equation is as follows:
TC = √(TP² + TP²) = √(6² + 6²) = √72 = 8.49 cm
Similarly, we can use the same equation to find the length of TD:
TD = √(DP² + DP²) = √(6² + 6²) = √72 = 8.49 cm
Therefore, the slope of TC is equal to 8.49 cm and the slope of TD is equal to 8.49 cm.
This is the solution to your problem. Remember, always double check your equations and use appropriate symbols for a clear solution. Happy geometry solving!
