Question

consider triangle ghj. what is the length of line segment hj? 5 units 5√3 units 10 units 10√3 units

Explanation:

Step1: Identify right triangle sides

Right triangle $GHJ$, right angle at $H$. Hypotenuse $JG=10$, leg $GH=5$.

Step2: Apply Pythagorean theorem

Let $HJ=x$. Use $a^2 + b^2 = c^2$:
$$x^2 + 5^2 = 10^2$$

Step3: Solve for $x$

Calculate squares:
$$x^2 + 25 = 100$$
Isolate $x^2$:
$$x^2 = 100 - 25 = 75$$
Take square root:
$$x = \sqrt{75} = 5\sqrt{3}$$

Answer:

$5\sqrt{3}$ units