Grade 10 · Geometry

Grade 10 Geometry — Right triangles / SOHCAHTOA questions and answers

Sine, cosine, and tangent — a huge US search. Written in American English for students, parents, and teachers in the United States.

Practice quiz

Question and answer list

Open a card to see the answer. These are original practice items for US elementary students — not a state test copy.

1. SOHCAHTOA: sine is

Answer: opposite / hypotenuse

Sin = O/H.

2. Cosine is

Answer: adjacent / hypotenuse

Cos = A/H.

3. Tangent is

Answer: opposite / adjacent

Tan = O/A.

4. In a right triangle, the hypotenuse is

Answer: the longest side, opposite 90°

Never use a leg as the hypotenuse in SOHCAHTOA.

5. If sin θ = 3/5, a possible opposite side is

Answer: 3 (with hypotenuse 5)

Keep the ratio.

6. A 30°-60°-90° triangle has sides

Answer: x, x√3, 2x

The side opposite 30° is the shortest.

7. A 45°-45°-90° triangle has legs

Answer: equal, and hypotenuse leg√2

It is isosceles.

8. To find an angle from two sides, use

Answer: inverse trig (sin⁻¹, cos⁻¹, tan⁻¹)

Calculators have SIN⁻¹.