← Math

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S3 · 中三 questions. Answer in your own words, then submit to get a score.

  1. 1. In triangle ABC, angle A = 88°, angle C = 35°, and side AB = 31 cm. Find the size of angle B and the length of side CA. Show your working.

  2. 2. In a triangle with angles 22°, 123°, and C, side AB (opposite angle C) is 19 cm. Find angle C and the length of side CA (opposite angle 22°).

  3. 3. In triangle ABC, angle A = 87°, angle C = 41°, and side AC = 22 cm. Find angle B and the length of side BC (opposite angle 41°).

  4. 4. In a triangle, side a = 7 units is opposite angle θ\theta, side b = 9.5 units is opposite angle 61°. Given that θ\theta is acute, find θ\theta using the sine rule.

  5. 5. Two angles in a triangle are 37° and θ\theta, with opposite sides 7 cm and 11 cm respectively. If θ\theta is acute, use the sine rule to find θ\theta.

Transcript
## Page 1 S5 Math CP Chapter 9 Applications of Trigonometry in 2-dimensional Problems Name ______________ Class __ ( ) 2 Solve the following triangles. [Nos. 7–9] 7. ![](https://i.imgur.com/placeholder.png) 88∘+35∘+B=180∘88^\circ + 35^\circ + B = 180^\circ B=57∘B = 57^\circ CAsin⁡57∘=31sin⁡88∘\frac{CA}{\sin 57^\circ} = \frac{31}{\sin 88^\circ} CA=26.0 cmCA = 26.0\,\text{cm} CBsin⁡35∘=31sin⁡88∘\frac{CB}{\sin 35^\circ} = \frac{31}{\sin 88^\circ} CB=17.8 cmCB = 17.8\,\text{cm} 8. ![](https://i.imgur.com/placeholder.png) 22∘+123∘+C=180∘22^\circ + 123^\circ + C = 180^\circ C=35∘C = 35^\circ 19sin⁡35∘=CAsin⁡22∘\frac{19}{\sin 35^\circ} = \frac{CA}{\sin 22^\circ} CA=12.9 cmCA = 12.9\,\text{cm} CBsin⁡123∘=19sin⁡35∘\frac{CB}{\sin 123^\circ} = \frac{19}{\sin 35^\circ} CB=27.8 cmCB = 27.8\,\text{cm} 9. ![](https://i.imgur.com/placeholder.png) B+87∘+41∘=180∘B + 87^\circ + 41^\circ = 180^\circ B=52∘B = 52^\circ 22sin⁡52∘=BCsin⁡41∘\frac{22}{\sin 52^\circ} = \frac{BC}{\sin 41^\circ} BC=18.3 cmBC = 18.3\,\text{cm} ABsin⁡87∘=22sin⁡51∘\frac{AB}{\sin 87^\circ} = \frac{22}{\sin 51^\circ} AB=27.9 cmAB = 27.9\,\text{cm} In each of the following triangles, find θ\theta. [Nos. 10–15] 10. ![](https://i.imgur.com/placeholder.png) 7sin⁡θ=9.5sin⁡61∘\frac{7}{\sin \theta} = \frac{9.5}{\sin 61^\circ} θ=40.1∘\theta = 40.1^\circ 11. ![](https://i.imgur.com/placeholder.png) 15.6sin⁡θ=19.3sin⁡43∘\frac{15.6}{\sin \theta} = \frac{19.3}{\sin 43^\circ} θ=33.5∘\theta = 33.5^\circ 12. θ\theta is acute. ![](https://i.imgur.com/placeholder.png) 11sin⁡θ=7sin⁡37∘\frac{11}{\sin \theta} = \frac{7}{\sin 37^\circ} θ=71.0∘\theta = 71.0^\circ