Topic · 3 games

Trigonometry: angles and sides

Trigonometry links angles with lengths. Start with right triangles, move on to angles of elevation and depression, then take sine and cosine around the full circle.

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3 games

PLAY NOW · 20

Loading Ramp: Find the Missing Side

A winch pulls boxes up a ramp onto a platform. Name the opposite, adjacent, and hypotenuse, pick the right ratio, and calculate the side that makes the ramp fit.

Right trianglesSine, cosine, tangent
Play Loading Ramp
Height of the ramp
h = L · sin θ
Ratios
tan θ = opp ÷ adj

PLAY NOW · 21

Lighthouse Rescue: Aim with Angles

A rescue drone flies in a straight line from the lighthouse to a ship. Find the angle of depression or elevation with the inverse functions, or the distance from a known angle.

Inverse functionsElevation and depression
Play Lighthouse Rescue
Angle of depression
tan α = H ÷ D
Back to the angle
α = tan⁻¹(H ÷ D)

PLAY NOW · 22

Ferris Wheel: Sine and Cosine on a Circle

A cabin rides a Ferris wheel past 90°, 180°, and beyond. Predict its coordinates with cosine and sine, find the signs in each quadrant, and earn a bonus for exact values.

Unit circleSpecial angles
Play Ferris Wheel
Cabin position
(R · cos θ, R · sin θ)
Special angle
sin 30° = 1/2

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