Question

Please help 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.)

Answer 1

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).