1 Answer

Dmytro Yashchenko · Answer 1 · 2023-08-07T04:20:50+0000

Step-by-step explanation:

We are given a right triangle and we need to find the length of the missing side, which in this case is the leg 'a' of the triangle.

Step 1. To solve this problem, since it is a right triangle, we use the Pythagorean theorem:

In this case, c and b are:

$\begin{gathered} c=√(85)mm \\ b=7mm \end{gathered}$

Step 2. From the formula of the Pythagorean theorem:

We solve for a:

$\begin{gathered} a^2=c^2-b^2 \\ \downarrow \\ a=√(c^2-b^2) \end{gathered}$

Step 3. Now that we have solved for a, we substitute the known values of c and b:

$a=\sqrt{(√(85))^2-(7)^2}$

Solving the operations we find the value of a:

$\begin{gathered} a=√(85+49) \\ \downarrow \\ a=√(36) \\ \downarrow \\ a=6mm \end{gathered}$

The length of the unknown leg is 6mm.

Answer:

6mm

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