Question

What is the length of the unknown leg in the right triangle?

Answer 1

Answer:

6mm

Step-by-step explanation:

In a right angled triangle if a and b is the length of  sides containing right angle, then length of hypotenuse  is given by $hypotenuse= \sqrt{a^2 + b^2}$ .

In the given problem a and b are a and 7mm respectively.

hypotenuse = $\sqrt{ 85}$

Using the formula for hypotenuse we have

$hypotenuse= \sqrt{a^2 + b^2}\\\\\=>\sqrt{85} = \sqrt{a^2 + 7^2} \\ squaring / both / side / we / have\\=>\sqrt{85}^2 = \sqrt{a^2 + 7^2}^2\\=>85 = a^2 + 49\\\\=> a^2 = 85-49 = 36\\=>\sqrt{a^2} = \sqrt{36} \\=> a = 6$

Thus, length of unknown leg is 6mm.