Geometry

SOHCAHTOA

Resize a triangle. Follow its ratios.

Predict, test and explain

Step 1 of 3

Predict

Keep the angle at 30°. If the hypotenuse doubles from 4 to 8, what happens to sin 30°?

sin⁡θ=oh≈0.574\sin\theta = \frac{o}{h} \approx 0.574
35∘35^\circ
adjacent≈4.91\text{adjacent} \approx 4.91
opposite≈3.44\text{opposite} \approx 3.44
h=6h = 6

Scroll the diagram sideways to see every label.

sin⁡θ≈0.574\sin\theta \approx 0.574cos⁡θ≈0.819\cos\theta \approx 0.819tan⁡θ≈0.7\tan\theta \approx 0.7

InvestigateResize the triangle. Which ratios stay the same?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Try it in the simulation. Change one thing at a time.

Notes and saved values stay in this tab. They disappear when you reload.

Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

In a right triangle, an acute angle has an opposite side of 3 cm and a hypotenuse of 6 cm. Find the angle.

Hint

Use sine: opposite divided by hypotenuse.

Reveal answer

The acute angle is 30 degrees.

sin⁡θ=36=12,θ=30∘\sin\theta=\frac{3}{6}=\frac12,\qquad\theta=30^\circ

Build an explanation

Hint 1

Choose an angle, then identify opposite, adjacent and hypotenuse.

Hint 2

Select the ratio using the sides you know or need.

Hint 3

Sine = opposite/hypotenuse; cosine = adjacent/hypotenuse; tangent = opposite/adjacent.

Worked example

This example uses fixed values, separate from the diagram controls.

A right triangle has angle 30° and hypotenuse 6 cm. Find the opposite side.

  1. Use sine because the sides are opposite and hypotenuse.
  2. sin 30° = opposite/6.
  3. Multiply by 6: opposite = 6 × 0.5.

Answer: 3 cm.

Connect this idea

Watch out: Opposite and adjacent depend on the chosen angle; the hypotenuse does not.