Question

put the steps in order: 30 - 60 - 90 #2
solve for x by putting the steps in order.
checker: ✗

x ≈ 2.9 units
√3 · x = 1 · √26
√3 · x = √26
x = √26 / √3
x / √26 = 1 / √3
short / medium = short / medium

Explanation:

Step1: Set up ratio

In a 30 - 60 - 90 triangle, the ratio of the sides is \( \frac{\text{short}}{\text{medium}}=\frac{\text{short}}{\text{medium}} \).

Step2: Substitute values

Substitute the side lengths into the ratio: \( \frac{x}{\sqrt{26}}=\frac{1}{\sqrt{3}} \).

Step3: Cross - multiply

Cross - multiply to get \( \sqrt{3}\cdot x = 1\cdot\sqrt{26} \), which simplifies to \( \sqrt{3}\cdot x=\sqrt{26} \).

Step4: Solve for \( x \)

Solve for \( x \) by \( x = \frac{\sqrt{26}}{\sqrt{3}} \).

Step5: Approximate \( x \)

Calculate \( x\approx2.9 \) units.

Answer:

1. \( \frac{\text{short}}{\text{medium}}=\frac{\text{short}}{\text{medium}} \)
2. \( \frac{x}{\sqrt{26}}=\frac{1}{\sqrt{3}} \)
3. \( \sqrt{3}\cdot x = 1\cdot\sqrt{26} \)
4. \( \sqrt{3}\cdot x=\sqrt{26} \)
5. \( x = \frac{\sqrt{26}}{\sqrt{3}} \)
6. \( x\approx2.9 \) units