SAT Math formula sheet · all 24 · Geometry and Trigonometry · #23 of 24

SOHCAHTOA on the SAT: How It Is Tested

Right triangles and trigonometry

Trigonometry diagram for the SAT: SOH CAH TOA and the Pythagorean theorem ONLY apply to right triangles. Use the Pythagorean theorem to find a missing sid
What it is really testingSOH CAH TOA and the Pythagorean theorem ONLY apply to right triangles. Use the Pythagorean theorem to find a missing side. Trig questions just want a ratio.

The question from the sheet

Hard
SAT Geometry and Trigonometryanswer 0.96
In triangle PQRPQR, cos⁡(Q)=1450\cos(Q) = \frac{14}{50} and angle PP is a right angle. What is the value of cos⁡(R)\cos(R)?
Student-produced response: 0.96

How the diagram applies

  1. PP is the right angle, so QQ and RR are the two acute angles and Q+R=90∘Q + R = 90^{\circ}. That makes cos⁡(R)=sin⁡(Q)\cos(R) = \sin(Q).
  2. cos⁡(Q)=1450\cos(Q) = \tfrac{14}{50} means adjacent 1414, hypotenuse 5050. Pythagorean theorem: opposite =502−142=2,304=48= \sqrt{50^{2} - 14^{2}} = \sqrt{2{,}304} = 48.
  3. cos⁡(R)=sin⁡(Q)=4850=0.96\cos(R) = \sin(Q) = \tfrac{48}{50} = 0.96.

Answer: 0.96

That is 1 of 24.

The whole sheet is one page per formula, each one solved on a real SAT question. Print it, stick it on the wall, scan any diagram to get back here.

Download the sheet (PDF)Watch this one solved →

The PDF needs no account. The video, the clean diagrams and practice on this skill need a free one, and never a card.

All 24 diagrams

Common Questions

It comes up as an SAT right triangles and trigonometry question. SOH CAH TOA and the Pythagorean theorem ONLY apply to right triangles. Use the Pythagorean theorem to find a missing side. Trig questions just want a ratio.

P is the right angle, so Q and R are the two acute angles and Q + R = 90°. That makes (R) = (Q). (Q) = 1450 means adjacent 14, hypotenuse 50. Pythagorean theorem: opposite = 50^2 - 14^2 = 2,304 = 48. (R) = (Q) = 4850 = 0.96.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Trigonometry is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.