Trigonometry on the SAT sticks to right triangles — no unit circle required. If you memorize SOH-CAH-TOA and know two special triangles, you're set.

SOH-CAH-TOA

For a right triangle with an acute angle :

Example 1: In a right triangle, the side opposite angle is 3 and the hypotenuse is 5. Find , , and .

First, find the adjacent side:

Special Right Triangles

These appear constantly on the SAT:

45-45-90 Triangle: sides are

30-60-90 Triangle: sides are

Example 2: In a 30-60-90 triangle, the shortest side is 5. Find the other sides.

Example 3: In a 45-45-90 triangle, the hypotenuse is 8. Find the legs.

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The Complementary Angle Relationship

This SAT favorite states:

Example 4: If , what is ?

Using Trig to Find Missing Sides

Example 5: A ladder leans against a wall at a 65° angle with the ground. If the ladder is 12 feet long, how high up the wall does it reach?


Using Trig to Find Angles

Example 6: In a right triangle, the opposite side is 7 and the adjacent side is 7. What is the angle?


Practice Problems

Problem 1: In a right triangle, the legs are 6 and 8. What is for the angle opposite the side of length 6?

Solution

Hypotenuse:

Problem 2: In a 30-60-90 triangle, the hypotenuse is 14. What is the length of the side opposite the 60° angle?

Solution

Shortest side = . Side opposite 60° = .

Problem 3: If and is acute, what is ?

Solution

Key Takeaways

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