Me! find the length of the unknown side of each triangle. give the exact length and an approximate length. a right triangle has one leg with unknown length, the other leg with length of 5 m, and the hypotenuse with length 13 times sqrt 5 m. the exact length of the unknown side is _ m. (simplify your answer. type an exact answer, using radicals as needed. use integers or decimals for any numbers in the expression.) the approximate length of the unknown side is _ m. (round to one decimal place as needed.)

A right triangle has one leg with unknown length, the other leg with length of 5 m, and the hypotenuse with length 13 times sqrt 5 m.

We can use the Pythagorean formula to find the other leg of the right triangle.

a²+b²=c²

Where a and b are the legs of the triangle and c is the hypotenuse.

According to the given problem,

one leg: a= 5m and hypotenuse: c=13√5 m.

So, we can plug in these values in the above equation to get the value of unknown side:b. Hence,

5²+b²=(13√5)²

25 + b² = 13²*(√5)²

25 + b² = 169* 5

25+ b² = 845

25 + b² - 25 = 845 - 25

b² = 820

b =√ 820

b = √(4*205)

b = √4 *√205

b = 2√205

b= 2* 14.32

b = 28.64

So, b= 28.6 (Rounded to one decimal place)

Hence, the exact length of the unknown leg is 2√205m or 28.6 m (approximately).

step-by-step explanation:

what grade level is this? need to know so i can look in my old textbooks!

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step-by-step explanation: