consider triangle ghj. what is the length of line segment hj? 5 units 5√3 units 10 units 10√3 units
consider triangle ghj. what is the length of line segment hj? 5 units 5√3 units 10 units 10√3 units
Answer
Answer:
B. $5\sqrt{3}$ units
Explanation:
Step1: Apply Pythagorean theorem
In right - triangle $GHJ$, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = GJ = 10$ (hypotenuse) and $a = GH=5$, and we want to find $b = HJ$. So $HJ=\sqrt{GJ^{2}-GH^{2}}$.
Step2: Substitute values
Substitute $GJ = 10$ and $GH = 5$ into the formula: $HJ=\sqrt{10^{2}-5^{2}}=\sqrt{100 - 25}=\sqrt{75}$.
Step3: Simplify the square - root
Simplify $\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}$.