LCAT Math, Geometry and Trigonometry
Right triangles and trigonometry on the LCAT
In a right triangle, a² + b² = c², with c the hypotenuse. From an acute angle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent (SOH-CAH-TOA). For complementary angles, sin(x) = cos(90° − x). π radians = 180°.
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No calculator on the LCAT. LUMS’s official guidelines say calculators are not allowed, so every practice question here can be solved by hand.
| Triangle | Sides |
|---|---|
| 45°-45°-90° | s, s, s√2 |
| 30°-60°-90° | x, x√3, 2x |
| Common triples | 3-4-5, 5-12-13, 8-15-17, 7-24-25 |
Label the sides O, A and H from the angle named in the question before choosing a ratio.
Common mistakes
Adding legs for the hypotenuse5 and 12 give 13, not 17.
Opposite vs adjacentOpposite is the side not touching the angle.
Special-triangle mix-upOpposite 60° is x√3; the hypotenuse is 2x.
Sample questions with answers
1. Legs 5 and 12. Hypotenuse?
- 17
- 13 (correct)
- 60
- 169
√(25 + 144) = 13.
2. Right angle at C, BC = 8, AC = 15, AB = 17. sin A?
- 15/17
- 8/17 (correct)
- 8/15
- 15/8
Opposite A is BC = 8; hypotenuse 17.
3. What is 60° in radians?
- π/6
- π/3 (correct)
- π/2
- 2π/3
60 × π/180 = π/3.
Frequently asked questions
What is SOH-CAH-TOA?
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
Why does sin(x) equal cos(90° − x)?
In a right triangle, the side opposite one acute angle is adjacent to the other.
Is right triangles and trig tested on the LCAT?
Yes. It falls under Geometry and Trigonometry, one of the content domains LUMS lists for the LCAT in its official sample questions.
Can I practice this without a calculator?
Yes. Every practice question here can be solved by hand, because calculators are not allowed on the LCAT.