ANGLE θ (°)
ACTIVE
GIVEN SIDE
TAP
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AUTO
RESULTS
AUTO
TRIANGLE SOLVER
Right triangle trig, sine rule and cosine rule with on-screen working
Useful for GCSE maths, trigonometry revision and triangle side or angle checks
WORKING
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PAGE SUMMARY
Use RIGHT for right triangle trig with one acute angle and one side.
Use SINE when you know two angles and one opposite side.
Use COS when you know two sides and the included angle.
This page is useful for trigonometry revision, homework checks and GCSE triangle questions.
Extra formulas, worked examples and related maths links are on the next pages.
Keep the calculator on Page 1 for fast entry and put the help content on separate pages.
RIGHT TRIANGLE MODE
Enter an acute angle and one side.
Then choose whether the known side is hypotenuse, adjacent or opposite.
sinθ = opp / hyp
cosθ = adj / hyp
tanθ = opp / adj
SINE RULE MODE
Use this when you know two angles and one opposite side.
a / sinA = b / sinB = c / sinC
C = 180 − A − B
COSINE RULE MODE
Use this when you know two sides and the included angle.
a² = b² + c² − 2bc cosA
a = √(a²)
KEYPAD HELP
NEXT moves to the next editable box.
BS deletes, CLR clears the current box and C resets the whole page.
ENTER solves the current triangle setup.
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WORKED EXAMPLE: RIGHT
Given θ = 30° and hypotenuse = 10
opp = 10 sin30 = 5
adj = 10 cos30 ≈ 8.66
Other angle = 60°
WORKED EXAMPLE: SINE
Given A = 40°, B = 60°, a = 12
C = 180 − 40 − 60 = 80°
b = 12 sin60 / sin40 ≈ 16.17
c = 12 sin80 / sin40 ≈ 18.39
WORKED EXAMPLE: COS
Given b = 7, c = 9, A = 30°
a² = 7² + 9² − 2×7×9 cos30
a² ≈ 20.88
a ≈ 4.57
WHEN TO USE WHICH RULE
RIGHT mode is for right triangles only.
SINE rule is best with an opposite side and known angles.
COS rule is best with two sides and the included angle.
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TRIANGLE SOLVER HELP
This page is designed for triangle side and angle calculations with clear working.
It suits searches for triangle solver, sine rule calculator, cosine rule calculator and right triangle trig calculator.
COMMON GCSE USES
Exam questions often ask for missing sides, angles and rule choice.
Checking whether to use sine rule, cosine rule or right triangle trig is part of the skill.
RELATED TELETEXT-TOOLS PAGES
LOOP BACK
Use NEXT to return to Page 1 and carry on solving triangles.
That keeps the calculator clear while still giving stronger help and SEO pages.
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ANGLE θ (°)
ACTIVE
GIVEN SIDE
TAP
—
AUTO
RESULTS
AUTO
WORKING
—
—
—
—
—
—
—
PAGE 1/4
RIGHT TRIANGLE
Enter one acute angle and one side.
Choose whether the known side is hypotenuse, adjacent or opposite.
sinθ = opp / hyp
cosθ = adj / hyp
tanθ = opp / adj
SINE RULE
a / sinA = b / sinB = c / sinC
C = 180 − A − B
COSINE RULE
a² = b² + c² − 2bc cosA
a = √(a²)
KEYPAD
NEXT moves box, BS deletes, CLR clears the current box and C resets the page.
Use ROUND for the number of decimal places shown in the answer.
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RIGHT EXAMPLE
θ = 30°, hyp = 10
opp = 10 sin30 = 5
adj = 10 cos30 ≈ 8.66
SINE EXAMPLE
A = 40°, B = 60°, a = 12
C = 80°
b ≈ 16.17, c ≈ 18.39
COS EXAMPLE
b = 7, c = 9, A = 30°
a² ≈ 20.88
a ≈ 4.57
RULE CHOICE
RIGHT is only for right triangles.
SINE is best when you know angles and an opposite side.
COS is best when you know two sides and the included angle.
PAGE 3/4
TRIANGLE SOLVER HELP
This page helps with right triangle trig, sine rule and cosine rule calculations.
It fits common GCSE maths revision and homework checking tasks.
SEARCH TOPICS
triangle solver
sine rule calculator
cosine rule calculator
right triangle trig calculator
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