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studyTrigonometry
CoreMaths revision

Solving Triangles

Solve triangles from mixed side-angle information, beginning with right triangles and extending to sine/cosine rules.

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Focus points
✓Solve right triangles.
✓Apply sine rule.
✓Apply cosine rule.
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Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions
Question 1FluencyCore
Original practice · Free Online Revision
Skill · right-triangle side
A right triangle has hypotenuse 10 cm and angle 37°. Find the side opposite the angle to 1 decimal place.
Question 2FluencyCore
Original practice · Free Online Revision
Skill · right-triangle angle
A right triangle has legs 7 cm and 9 cm. Find the angle opposite the 7 cm side.
Question 3FluencyCore
Original practice · Free Online Revision
Skill · angle sum
In triangle ABC, a=8, A=35°, B=62°. Find C.
Question 4FluencyCore
Original practice · Free Online Revision
Skill · sine rule
Using a=8, A=35°, B=62°, find b to 2 d.p.
Question 5FluencyCore
Original practice · Free Online Revision
Skill · cosine rule
Two sides are 7 cm and 10 cm with included angle 60°. Find the third side.
Question 6FluencyCore
Original practice · Free Online Revision
Skill · cosine rule angle
Triangle sides are 5,7,9. Find the angle opposite side 9.
Question 7ApplicationStretch
Original practice · Free Online Revision
Skill · area of triangle
A surveyor measures two sides from a point as 120 m and 85 m with included angle 47°. Find the area.
Question 8ReasoningStretch
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Skill · ambiguous case
Explain the ambiguous case in the sine rule when given SSA data.