Year 11 in England

10th grade trigonometry

8 10th grade trigonometry skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.

Mixed review

Ten questions drawn from every skill below.

Print a review worksheet Riddle puzzle on screen Bingo

Trigonometric ratios: SOH CAH TOA

CCSS HSG.SRT.C.6CCSS HSG.SRT.C.8England: GCSE Foundation GeometryEngland: GCSE Higher Geometry

Example

A ramp rises at 64° over a horizontal distance of 10 m. How high does it rise? Give 1 decimal place.

10 × tan 64° = 20.503
≈ 20.5 m

Answer: 20.5

Builds on: Pythagoras' theorem, Similar shapes

Leads to: Pythagoras and trigonometry in 3D, Find angles with inverse trig, Exact trig values (0°, 30°, 45°, 60°, 90°), Angles of elevation and depression

Print a worksheet ✏️ Write on screen Flashcards

Find angles with inverse trig

CCSS HSG.SRT.C.8England: GCSE Higher Geometry

Example

A right triangle has opposite side 7 cm and adjacent side 14 cm to angle θ. Find θ to 1 decimal place.

tan θ = 7/14
θ = tan⁻¹(7/14) ≈ 26.6°

Answer: 26.6

Builds on: Trigonometric ratios: SOH CAH TOA

Leads to: The sine rule (law of sines), Solve trigonometric equations, Find an angle with the sine rule

Print a worksheet ✏️ Write on screen Flashcards

Exact trig values (0°, 30°, 45°, 60°, 90°)

CCSS HSF.TF.A.3England: GCSE Higher Geometry

Example

What is the exact value of tan 30°?

tan 30° = √3/3

Answer: √3/3

Builds on: Trigonometric ratios: SOH CAH TOA, Simplify surds (radicals)

Leads to: The unit circle and radians, Find exact side lengths using 30°, 45° and 60°, Read exact coordinates on the unit circle

Print a worksheet ✏️ Write on screen Flashcards

Angles of elevation and depression

CCSS HSG.SRT.C.8England: GCSE Foundation GeometryEngland: GCSE Higher Geometry

Example

Maya stands 19 m from the base of a tower. The angle of elevation to the top is 17°. How tall is the tower, to the nearest metre? (Ignore Maya's height.)

h = 19 × tan 17° ≈ 5.81
≈ 6 m

Answer: 6

Builds on: Trigonometric ratios: SOH CAH TOA

Print a worksheet ✏️ Write on screen Flashcards

Label hypotenuse, opposite and adjacent sides

CCSS HSG.SRT.C.6England: GCSE Foundation Geometry

Example

In triangle YPN, the right angle is at P. Using angle Y, which side is the adjacent?

Answer: YP

Builds on: Pythagoras' theorem

Leads to: Choose sine, cosine or tangent for a problem

Print a worksheet ✏️ Write on screen Flashcards

Choose sine, cosine or tangent for a problem

CCSS HSG.SRT.C.8England: GCSE Foundation GeometryEngland: GCSE Higher Geometry

Example

In a right triangle you know angle θ and the hypotenuse. You want the adjacent side. Which ratio should you use?

Answer: cos

Builds on: Label hypotenuse, opposite and adjacent sides

Print a worksheet ✏️ Write on screen Flashcards

Find a side when it is on the bottom of the trig ratio

CCSS HSG.SRT.C.8England: GCSE Higher Geometry

Example

In a right triangle, the side adjacent to a 52° angle is 19 cm. Find the hypotenuse to 1 decimal place.

H = 19 ÷ cos 52°
≈ 30.9 cm

Answer: 30.9

Builds on: Trigonometric ratios: SOH CAH TOA

Print a worksheet ✏️ Write on screen Flashcards

Find exact side lengths using 30°, 45° and 60°

CCSS HSG.SRT.C.6CCSS HSG.SRT.C.8England: GCSE Higher Geometry

Example

A right triangle has two equal sides of 9 cm and a 45° angle. Find the hypotenuse. Give an exact answer.

9 ÷ (√2/2) = 9√2
9√2 cm

Answer: 9√2

Builds on: Exact trig values (0°, 30°, 45°, 60°, 90°)

Print a worksheet ✏️ Write on screen Flashcards

Keep exploring

Math, English and science that click.