Question

for the given triangle, find the missing lengths. give an exact answer and, where appropriate, an approximation to three decimal places. find the length of the other leg. select the correct choice below and fill in the answer box(es) to complete your choice. a. using radicals, the exact length of the other leg is \\(\square\\) units. the approximate length of the other leg, up to three decimal places, is \\(\square\\) units. (simplify your answers.) b. the exact length of the other leg is \\(\square\\) units. no approximation is necessary. (type an integer or a decimal) triangle image: right triangle with one angle 45°, one leg 5, hypotenuse? and the other leg?

Explanation:

Step1: Identify the triangle type

This is a \(45 - 45-90\) right - triangle. In a \(45 - 45-90\) triangle, the legs are equal in length. Let the length of the unknown leg be \(x\).

Step2: Apply the Pythagorean theorem (alternative way, but we can also use the property of \(45 - 45-90\) triangle)

For a \(45 - 45-90\) triangle, if the length of one leg is \(a\), the length of the hypotenuse \(c=a\sqrt{2}\). But since we are looking for the leg and we know one leg, and using the fact that in a \(45 - 45-90\) triangle \(x = 5\) (exact value). The approximation is also \(5.000\) (since \(5\) is an integer and to three decimal places \(5=5.000\)).

Answer:

A. Using radicals, the exact length of the other leg is \(5\) units. The approximate length of the other leg, up to three decimal places, is \(5.000\) units.