Question

Math

Posted 3 months ago

```
In the right triangle shown, $m \angle J=60^{\circ}$ and $J L=6 \sqrt{3}$.
How long is $J K$ ?
Choose 1 answer:
(A) 3
(B) $2 \sqrt{3}$
(C) $3 \sqrt{3}$
(D) 6
(E) 9
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 2

In a 30-60-90 triangle, the ratio of the lengths of the sides opposite the 30°, 60°, and 90° angles is 1: $\sqrt{3}$: 2

step 3

Since $JL$ is opposite the 60° angle, and its length is $6\sqrt{3}$, we can find the length of $JK$ (opposite the 90° angle) by multiplying the length of $JL$ by $\frac{2}{\sqrt{3}}$

step 4

Calculating the length of $JK$: $JK = 6\sqrt{3} \times \frac{2}{\sqrt{3}} = 6 \times 2 = 12$. However, since $JK$ is the hypotenuse, we need to divide by 2 to get the length of the side opposite the 30° angle

step 5

Therefore, the length of $JK$ is $12 \div 2 = 6$

D

Key Concept

30-60-90 right triangle side ratios

Explanation

In a 30-60-90 triangle, the length of the side opposite the 60° angle is $\sqrt{3}$ times the length of the side opposite the 30° angle, and the length of the hypotenuse is twice the length of the side opposite the 30° angle.

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