Question

What is the length of the missing leg?

Answer 1

Answer:

$a=\sqrt{609}\\\\a\approx 24.67793$

Step-by-step explanation:

To solve for the leg of the missing right triangle, one must use the Pythagorean theorem. The Pythagorean theorem states the following,

$a^2+b^2=c^2$

Where (a) and (b) are the sides adjacent to or next to the right angle. (c) is the side opposite the right angle. Substitute in the given values and solve for the unknown,

$a^2+b^2=c^2$

Substitute,

$a^2+40^2=47^2$

Simplify,

$a^2+1600=2209$

Inverse operations,

$a^2=609$

$a=\sqrt{609}\\\\a\approx 24.67793$

Answer 2

Answer:

b = 9 mm

Step-by-step explanation:

Using Pythagoras; identity in the right triangle

b² + 40² = 41²

b² + 1600 = 1681 ( subtract 1600 from both sides )

b² = 81 ( take the square root of both sides )

b = $\sqrt{81}$ = 9 mm