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Special Right Triangles: 45-45-90 & 30-60-90 — Easy Worksheet 1
Grade 10 · Whoobee Name: ____________________ Date: __________
Find x. Write answers in simplest radical form, like 5√3.
How to solve
In a 45°-45°-90° triangle the legs are equal and the hypotenuse is leg × √2. In a 30°-60°-90° triangle, if the short leg (opposite 30°) is s, the long leg is s√3 and the hypotenuse is 2s. Find the short leg (or the leg) first, then multiply. To undo √2 or √3, divide and rationalize: 10 ÷ √2 = 5√2.
Example
Find x.
Answer: 3√2
Not quite. The answer is
💡 In a 45°-45°-90° triangle with leg a, the other leg is also a and the hypotenuse is a√2. The leg is 3, so x = 3 × √2 = 3√2.
✓ Correct!
Not quite. The answer is
💡 In a 45°-45°-90° triangle with leg a, the other leg is also a and the hypotenuse is a√2. The leg is 3, so x = 3 × √2 = 3√2.
💡 How to solve: Special Right Triangles: 45-45-90 & 30-60-90
In a 45°-45°-90° triangle the legs are equal and the hypotenuse is leg × √2. In a 30°-60°-90° triangle, if the short leg (opposite 30°) is s, the long leg is s√3 and the hypotenuse is 2s. Find the short leg (or the leg) first, then multiply. To undo √2 or √3, divide and rationalize: 10 ÷ √2 = 5√2.
Try a similar one
Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The short leg is 4, so the hypotenuse is x = 2 × 4 = 8.
✓ Correct!
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The short leg is 4, so the hypotenuse is x = 2 × 4 = 8.
💡 How to solve: Special Right Triangles: 45-45-90 & 30-60-90
In a 45°-45°-90° triangle the legs are equal and the hypotenuse is leg × √2. In a 30°-60°-90° triangle, if the short leg (opposite 30°) is s, the long leg is s√3 and the hypotenuse is 2s. Find the short leg (or the leg) first, then multiply. To undo √2 or √3, divide and rationalize: 10 ÷ √2 = 5√2.
Try a similar one
Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The short leg is 8, so the long leg is x = 8 × √3 = 8√3.
✓ Correct!
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The short leg is 8, so the long leg is x = 8 × √3 = 8√3.
💡 How to solve: Special Right Triangles: 45-45-90 & 30-60-90
In a 45°-45°-90° triangle the legs are equal and the hypotenuse is leg × √2. In a 30°-60°-90° triangle, if the short leg (opposite 30°) is s, the long leg is s√3 and the hypotenuse is 2s. Find the short leg (or the leg) first, then multiply. To undo √2 or √3, divide and rationalize: 10 ÷ √2 = 5√2.
Try a similar one
Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 In a 45°-45°-90° triangle with leg a, the other leg is also a and the hypotenuse is a√2. The leg is 2, so x = 2 × √2 = 2√2.
✓ Correct!
Not quite. The answer is
💡 In a 45°-45°-90° triangle with leg a, the other leg is also a and the hypotenuse is a√2. The leg is 2, so x = 2 × √2 = 2√2.
💡 How to solve: Special Right Triangles: 45-45-90 & 30-60-90
In a 45°-45°-90° triangle the legs are equal and the hypotenuse is leg × √2. In a 30°-60°-90° triangle, if the short leg (opposite 30°) is s, the long leg is s√3 and the hypotenuse is 2s. Find the short leg (or the leg) first, then multiply. To undo √2 or √3, divide and rationalize: 10 ÷ √2 = 5√2.
Try a similar one
Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The hypotenuse is 4, so the short leg is x = 4 ÷ 2 = 2.
✓ Correct!
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The hypotenuse is 4, so the short leg is x = 4 ÷ 2 = 2.
💡 How to solve: Special Right Triangles: 45-45-90 & 30-60-90
In a 45°-45°-90° triangle the legs are equal and the hypotenuse is leg × √2. In a 30°-60°-90° triangle, if the short leg (opposite 30°) is s, the long leg is s√3 and the hypotenuse is 2s. Find the short leg (or the leg) first, then multiply. To undo √2 or √3, divide and rationalize: 10 ÷ √2 = 5√2.
Try a similar one
Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The short leg is 5, so the long leg is x = 5 × √3 = 5√3.
✓ Correct!
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The short leg is 5, so the long leg is x = 5 × √3 = 5√3.
💡 How to solve: Special Right Triangles: 45-45-90 & 30-60-90
In a 45°-45°-90° triangle the legs are equal and the hypotenuse is leg × √2. In a 30°-60°-90° triangle, if the short leg (opposite 30°) is s, the long leg is s√3 and the hypotenuse is 2s. Find the short leg (or the leg) first, then multiply. To undo √2 or √3, divide and rationalize: 10 ÷ √2 = 5√2.
Try a similar one
Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 In a 45°-45°-90° triangle with leg a, the other leg is also a and the hypotenuse is a√2. The hypotenuse is 8√2, so the leg is x = 8√2 ÷ √2 = 8.
✓ Correct!
Not quite. The answer is
💡 In a 45°-45°-90° triangle with leg a, the other leg is also a and the hypotenuse is a√2. The hypotenuse is 8√2, so the leg is x = 8√2 ÷ √2 = 8.
💡 How to solve: Special Right Triangles: 45-45-90 & 30-60-90
In a 45°-45°-90° triangle the legs are equal and the hypotenuse is leg × √2. In a 30°-60°-90° triangle, if the short leg (opposite 30°) is s, the long leg is s√3 and the hypotenuse is 2s. Find the short leg (or the leg) first, then multiply. To undo √2 or √3, divide and rationalize: 10 ÷ √2 = 5√2.
Try a similar one
Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The short leg is 7, so the hypotenuse is x = 2 × 7 = 14.
✓ Correct!
Not quite. The answer is
💡 In a 30°-60°-90° triangle with short leg a (opposite 30°), the long leg (opposite 60°) is a√3 and the hypotenuse is 2a. The short leg is 7, so the hypotenuse is x = 2 × 7 = 14.
💡 How to solve: Special Right Triangles: 45-45-90 & 30-60-90
In a 45°-45°-90° triangle the legs are equal and the hypotenuse is leg × √2. In a 30°-60°-90° triangle, if the short leg (opposite 30°) is s, the long leg is s√3 and the hypotenuse is 2s. Find the short leg (or the leg) first, then multiply. To undo √2 or √3, divide and rationalize: 10 ÷ √2 = 5√2.
Try a similar one
Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Special Right Triangles: 45-45-90 & 30-60-90 — Easy Worksheet 1
Find x. Write answers in simplest radical form, like 5√3.