Question

What is the value of x? Round to the nearest tenth. Please Help

Answer 1

Answer:

x = 6.5 cm

Step-by-step explanation:

The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.

Use the Pythagorean theorem:

$leg^2+leg^2=hypotenuse^2$

We have

$leg=x,\ leg=20.2cm,\ hypotenuse=(14.7+x)cm$

Substitute:

$x^2+20.2^2=(14.7+x)^2$           use (a + b)² = a² + 2ab + b²

$x^2+408.04=14.7^2+(2)(14.7)(x)+x^2$          subtract x² from both sides

$408.04=216.09+29.4x$        subtract 216.09 from both sides

$191.95=29.4x$         divide both sides by 29.4

$x\approx6.5\ cm$