SOHCAHTOA%20MA - Right-angled triangles trigonometry practice (answers to 3 s.f./1 d.p.)

Sep 5, 2026

Trigonometry practice focused on solving right-angled triangle problems using sine, cosine and tangent. Tasks include finding missing side lengths and calculating marked angles from given right angles plus additional acute angles, with measurements provided in cm or m. Each question specifies precision requirements such as three significant figures or one decimal place, and typically references diagram-based relationships using expressions like tan(36), sin(60) and cos(43).

LanguageEnglish

CategoryExam

FormatPDF

Pages7

Reading Time18 min

AccessFree to download

Trigonometry problems using SOHCAHTOA

Right-angled triangle: find side lengths

Right-angled triangle: find angles and missing values

Quadrilateral angle/length calculation

1. ABC is a right-angled triangle. Angle B=90°. Angle A=36°. AB=8.7 cm. Work out the length of BC.Give your answer correct to 3 significant figures. 2. Calculate the value ofx.Give your answer correct to 3 significant figures. Diagram NOTx= 8,7×tan(36SUH AH TOA accurately drawn 6.32 (3 marks) Diagram NOT accurately drawn s 所 x=32×sin60) x=27.7 Ω7. (3marks) PQR is a triangle. Angle Q=90°. Angle R=43°. PR=5.8m. Calculate the length of QR.Give your answer correct to 3 significant figures. PQR is a triangle. Angle PQR=90°. PQ=12.5 cm. QR=5cm. Calculate the value ofx.Give your answer correct to 1 decimal place. 58 cos43)=C (3 marks) (3 marks) LMN is a right-angled triangle.MN=9.6 cm.LM=6.4 cm. Calculate the size of the angle markedx.Give your answer correct to 1 decimal place. 6. Work out the value ofx.Give your answer correct to 1 decimal place. (3 marks) Diagram NOT accurately drawn Diagram NOT accurately drawn PR=12 cm. QR=4.5 cm. Angle PRQ=90°. Work out the value ofxGive your answer correct to one decimal place. 8. Calculate the size of angle ain this right-angled triangle.Give your answer correct to 3 significant figures. =20.6 x=…20.………(3marks) Diagram NOT accurately drawn tan(=5 39.8 (3 marks) 9. PQR is a right-angled triangle. 8 cm PR=8cm. QR=12cm. (a)Find the size of the angle marked x.Give your answer correct to 1 decimal place. XYZ is a different right-angled triangle. XY=5cm. Angle Z=32. (b)Calculate the length YZ. Give your answer correct to 3 significant figures. Diagram NOT accurately drawn ⑥ S04 CAT T04 33.7。 (3) Diagram NOT accurately drawn So .….cm 9.44 .x=9. (3)(6marks) 10. The diagram shows a quadrilateral ABCD. AB=16 cm.AD=12 cm.Angle BCD=40°.Angle ADB=angle CBD=90°. Calculate the length of CD.Give your answer correct to 3 significant figures. 47BD=162-1 So Io x=1. Diagram NOT accuratcly drawn (5marks) 16. Diagram NOT accurately drawn ABC is a triangle. ADCis a straight line with BD perpendicular to AC.AB=7cm.BC=12 cm.Angle BAD=65°. Calculate the length of AC.Give your answer correct to 3 significant figures. CD²+6344 (6 marks)=(3·144858S

FAQs

How are the triangle problems solved in these questions?

They use sine, cosine and tangent relationships for right-angled triangles, matching the given angles and side lengths to trigonometric ratios.

What answer accuracy is required for the calculations?

Several questions require answers to 3 significant figures, while others require answers to 1 decimal place.

What types of values do the questions ask you to find?

The questions ask for missing side lengths and for the size of marked angles (often alongside additional sub-parts in the same problem).

Sep 5, 2026

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