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SAT Math skill page

SAT Right Triangles Practice

Use Pythagorean triples and special triangle patterns to solve right-triangle questions quickly.

Practice right triangles in Dolphin Try examples
10-16 min practice time 3 examples on page Geometry and Trigonometry
Practice time 10-16 min
On-page examples 3 examples
Best for Geometry and Trigonometry

What this tests

What to know for this SAT skill

Practice examples

Try a few SAT-style questions

Example 1 Easy

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

  1. 10
  2. 12
  3. 14
  4. 16
Show answer and explanation

Answer: 10

Use a^2 + b^2 = c^2. Since 6^2 + 8^2 = 36 + 64 = 100, the hypotenuse is 10.

Example 2 Medium

In a 30-60-90 triangle, the shortest side has length 5. What is the hypotenuse?

  1. 5
  2. 5sqrt(2)
  3. 10
  4. 10sqrt(3)
Show answer and explanation

Answer: 10

In a 30-60-90 triangle, the hypotenuse is twice the shortest side. Therefore the hypotenuse is 10.

Example 3 Hard

A 13-foot ladder leans against a wall. The base of the ladder is 5 feet from the wall. How high up the wall does the ladder reach?

  1. 8
  2. 10
  3. 12
  4. 18
Show answer and explanation

Answer: 12

The ladder is the hypotenuse. Use 5^2 + h^2 = 13^2, so 25 + h^2 = 169. Then h^2 = 144 and h = 12.

Avoid these traps

Common mistakes on this skill

Using the hypotenuse as a leg

The hypotenuse is always opposite the right angle and is the longest side.

Forgetting to square side lengths

The Pythagorean theorem uses squared side lengths, not the side lengths added directly.

Missing common triples

Recognizing 3-4-5, 5-12-13, and 8-15-17 patterns saves time.

Study plan

How to practice this skill in Dolphin

  1. Identify the hypotenuse before writing the equation.
  2. Practice common triples until they are automatic.
  3. Memorize 30-60-90 and 45-45-90 side relationships.
  4. Draw a quick triangle for word problems involving ladders, shadows, or distances.
Practice right triangles in Dolphin

Related practice

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Skill cluster

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FAQ

Questions about SAT Right Triangles Practice

Do right triangles appear often on SAT Math?

Yes. They show up in geometry, coordinate geometry, and word problems involving distance.

Which right triangle facts should I memorize?

Know the Pythagorean theorem, common triples, and the side ratios for 30-60-90 and 45-45-90 triangles.

How can I avoid right-triangle mistakes?

Mark the hypotenuse first, then decide whether the problem needs a formula, a triple, or a special-triangle ratio.