Question

there is a geometric figure composed of two right triangles. the left right triangle has a hypotenuse of length 10 and one leg of length 7. the right right triangle has one leg of length 3 and the other leg is ( x ), and the common leg of the two right triangles is the vertical side. we need to find the value of ( x ).

Explanation:

Step1: Find shared vertical side

Let the shared vertical side be $h$. Use Pythagoras on left triangle:
$h^2 = 10^2 - 7^2$
$h^2 = 100 - 49 = 51$

Step2: Solve for $x$ using Pythagoras

Use Pythagoras on right triangle:
$x^2 = h^2 - 3^2$
$x^2 = 51 - 9 = 42$
$x = \sqrt{42}$

Answer:

$\sqrt{42}$