Picture a smaller right triangle inside the big one. Its base is 41 (from sneaky Pythagoras!), and its height is 36. Use Pythagoras again on the big triangle, , the missing side leaps out as 41 inches .
The strategy to solve this problem is to first find the length of the bottom horizontal side of the triangle. Then, we can use the Pythagorean theorem to solve for the missing length of the hypotenuse.
Steps to solve:
1. Look at the right triangle on the left side of the diagram. We are given that the length of the vertical leg is 36 inches and the hypotenuse is 48 inches. We can use the Pythagorean theorem to solve for the missing length of the horizontal leg (x):
x^2 + 36^2 = 48^2
x^2 = 1584
x = √1584 ≈ 41 inches
2. Now that we know the length of the bottom horizontal side of the triangle (41 inches), we can use the Pythagorean theorem again to solve for the missing length of the hypotenuse on the right side of the diagram (which is also the missing length indicated in the question):
missing length^2 + 36^2 = 48^2
missing length^2 = 1584
missing length ≈ 41 inches
Therefore, the missing length indicated in the diagram is 41 inches.