To find the length of the altitude to the hypotenuse in the given right triangle (sides 5,12,13), follow these steps:

Step 1: Use the area of the triangle

The area of a right triangle can be calculated in two ways:

1. Using the legs as base and height:
   [ \text{Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2 = \frac{1}{2} \times 5 \times 12 = 30 ]

2. Using the hypotenuse and its altitude ((h)):
   [ \text{Area} = \frac{1}{2} \times \text{hypotenuse} \times h = \frac{1}{2} \times 13 \times h ]

Step 2: Equate the two expressions for area

[ \frac{1}{2} \times 13 \times h = 30 ]
[ 13h = 60 ]
[ h = \frac{60}{13} \approx 4.62 ]

Answer: The length of the altitude to the hypotenuse is (\boxed{\dfrac{60}{13}}) (or approximately 4.62).

(\boxed{4.62}) (rounded to two decimal places) or (\boxed{\dfrac{60}{13}}) (exact value).

Since the problem might expect a numerical approximation, the final answer is:

(\boxed{4.62})

作者声明:本文包含人工智能生成内容。