Worksheet 30 60 90 Prepdoc Bloomhs Form - Fill Out and Sign ... - Free Printable

Since all options (ExplainAnswer, TeachTopic, GeneratePractice) are false, I will only provide the final answer — but first, I must solve the problem accurately.

The worksheet is titled “30-60-90 Prep” and asks to find the missing two sides for each figure, leaving answers in rationalized and simplified form.

All triangles shown are 30°–60°–90° right triangles, which have a fixed side ratio:

- Short leg (opposite 30°) = $ x $
- Long leg (opposite 60°) = $ x\sqrt{3} $
- Hypotenuse (opposite 90°) = $ 2x $

We identify which side is given in each triangle, then compute the other two using this ratio.

Let’s go one by one. I’ll label them as in the worksheet: (1) through (15).

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(1)
Given: short leg = 3 (opposite 30°)
→ long leg = $ 3\sqrt{3} $
→ hypotenuse = $ 2 \cdot 3 = 6 $
✔ Missing sides: $ 3\sqrt{3},\ 6 $

(2)
Given: hypotenuse = 8
→ short leg = $ \frac{8}{2} = 4 $
→ long leg = $ 4\sqrt{3} $
✔ Missing: $ 4,\ 4\sqrt{3} $

(3)
Given: long leg = 4 (opposite 60°)
So $ x\sqrt{3} = 4 \Rightarrow x = \frac{4}{\sqrt{3}} = \frac{4\sqrt{3}}{3} $
→ short leg = $ \frac{4\sqrt{3}}{3} $
→ hypotenuse = $ 2x = \frac{8\sqrt{3}}{3} $
✔ Missing: $ \frac{4\sqrt{3}}{3},\ \frac{8\sqrt{3}}{3} $

(4)
Given: hypotenuse = 10
→ short leg = 5
→ long leg = $ 5\sqrt{3} $
✔ Missing: $ 5,\ 5\sqrt{3} $

(5)
Given: short leg = 5
→ long leg = $ 5\sqrt{3} $
→ hypotenuse = 10
✔ Missing: $ 5\sqrt{3},\ 10 $

(6)
Given: long leg = $ 5\sqrt{3} $
So $ x\sqrt{3} = 5\sqrt{3} \Rightarrow x = 5 $
→ short leg = 5
→ hypotenuse = 10
✔ Missing: $ 5,\ 10 $

(7)
Given: short leg = 12
→ long leg = $ 12\sqrt{3} $
→ hypotenuse = 24
✔ Missing: $ 12\sqrt{3},\ 24 $

(8)
Given: hypotenuse = $ 2\sqrt{3} $
→ short leg = $ \frac{2\sqrt{3}}{2} = \sqrt{3} $
→ long leg = $ \sqrt{3} \cdot \sqrt{3} = 3 $
✔ Missing: $ \sqrt{3},\ 3 $

(9)
Given: long leg = $ 3\sqrt{3} $
So $ x\sqrt{3} = 3\sqrt{3} \Rightarrow x = 3 $
→ short leg = 3
→ hypotenuse = 6
✔ Missing: $ 3,\ 6 $

(10)
Given: short leg = 10
→ long leg = $ 10\sqrt{3} $
→ hypotenuse = 20
✔ Missing: $ 10\sqrt{3},\ 20 $

(11)
Given: hypotenuse = 14
→ short leg = 7
→ long leg = $ 7\sqrt{3} $
✔ Missing: $ 7,\ 7\sqrt{3} $

(12)
Given: long leg = 6
So $ x\sqrt{3} = 6 \Rightarrow x = \frac{6}{\sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3} $
→ short leg = $ 2\sqrt{3} $
→ hypotenuse = $ 4\sqrt{3} $
✔ Missing: $ 2\sqrt{3},\ 4\sqrt{3} $

(13)
Given: short leg = 8
→ long leg = $ 8\sqrt{3} $
→ hypotenuse = 16
✔ Missing: $ 8\sqrt{3},\ 16 $

(14)
Given: hypotenuse = $ 8\sqrt{3} $
→ short leg = $ \frac{8\sqrt{3}}{2} = 4\sqrt{3} $
→ long leg = $ 4\sqrt{3} \cdot \sqrt{3} = 4 \cdot 3 = 12 $
✔ Missing: $ 4\sqrt{3},\ 12 $

(15)
Given: long leg = 9
So $ x\sqrt{3} = 9 \Rightarrow x = \frac{9}{\sqrt{3}} = \frac{9\sqrt{3}}{3} = 3\sqrt{3} $
→ short leg = $ 3\sqrt{3} $
→ hypotenuse = $ 2x = 6\sqrt{3} $
✔ Missing: $ 3\sqrt{3},\ 6\sqrt{3} $

Now, since the instruction says “Find the measure of the missing 2 sides for each figure below. Leave answer in: rationalized and simplified form.” — and the student is expected to write both missing sides per triangle — but the user only asked to solve the problem, not list all 15×2 answers explicitly unless required.

However, the response format says:
→ If options are false, *only* provide the Final Answer.

But what is the “final answer”? The problem has 15 items, each with 2 missing sides. Since no specific item was singled out, and the prompt says “Solve the problem accurately”, it's implied we need to provide all answers — but the format restriction says if options are false, only give Final Answer (no explanations).

Given ambiguity, and that the user uploaded a worksheet expecting answers for all 15, and the instruction says “ONLY THEN provide the final answer”, I will compile the answers as a clean list — since that is the only output allowed.

Let me format each as:
(1) $3\sqrt{3},\ 6$
(2) $4,\ 4\sqrt{3}$
(3) $\frac{4\sqrt{3}}{3},\ \frac{8\sqrt{3}}{3}$
(4) $5,\ 5\sqrt{3}$
(5) $5\sqrt{3},\ 10$
(6) $5,\ 10$
(7) $12\sqrt{3},\ 24$
(8) $\sqrt{3},\ 3$
(9) $3,\ 6$
(10) $10\sqrt{3},\ 20$
(11) $7,\ 7\sqrt{3}$
(12) $2\sqrt{3},\ 4\sqrt{3}$
(13) $8\sqrt{3},\ 16$
(14) $4\sqrt{3},\ 12$
(15) $3\sqrt{3},\ 6\sqrt{3}$

All are rationalized and simplified.

Final Answer:
(1) $3\sqrt{3},\ 6$
(2) $4,\ 4\sqrt{3}$
(3) $\frac{4\sqrt{3}}{3},\ \frac{8\sqrt{3}}{3}$
(4) $5,\ 5\sqrt{3}$
(5) $5\sqrt{3},\ 10$
(6) $5,\ 10$
(7) $12\sqrt{3},\ 24$
(8) $\sqrt{3},\ 3$
(9) $3,\ 6$
(10) $10\sqrt{3},\ 20$
(11) $7,\ 7\sqrt{3}$
(12) $2\sqrt{3},\ 4\sqrt{3}$
(13) $8\sqrt{3},\ 16$
(14) $4\sqrt{3},\ 12$
(15) $3\sqrt{3},\ 6\sqrt{3}$