Grade 10 · Geometry & measurement

Special right triangles practice

Special right triangles is a grade 10 math skill aligned to Common Core standard HSG.SRT.C.8: use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 special right triangles problems our math games drill.

CCSS HSG.SRT.C.815 questions in the bank

Sample questions

Try 8 for free

Question 1easy

In a $30$ - $60$ - $90$ triangle the hypotenuse is $14$ . What is the short leg?

The short leg is half the hypotenuse: $\dfrac{14}{2} = 7$ .

Question 2easy

In a $45$ - $45$ - $90$ triangle one leg is $12$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $12$ .

Question 3easy

In a $30$ - $60$ - $90$ triangle the short leg is $8$ . What is the hypotenuse?

The hypotenuse is twice the short leg: $2 \times 8 = 16$ .

Question 4easy

In a $45$ - $45$ - $90$ triangle one leg is $7$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $7$ .

Question 5easy

In a $30$ - $60$ - $90$ triangle the short leg is $3$ . What is the hypotenuse?

The hypotenuse is twice the short leg: $2 \times 3 = 6$ .

Question 6easy

In a $45$ - $45$ - $90$ triangle one leg is $15$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $15$ .

Question 7easy

In a $30$ - $60$ - $90$ triangle the short leg is $10$ . What is the hypotenuse?

The hypotenuse is twice the short leg: $2 \times 10 = 20$ .

Question 8easy

In a $45$ - $45$ - $90$ triangle one leg is $20$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $20$ .

Tests that cover special right triangles:

NAEP SBAC ACT LEAP 2025 NY State Math

More Grade 10 skills:

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