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

  1. 1. In a triangle with angles 50∘50^\circ, 30∘30^\circ, and a side of length 4 cm4\ \text{cm} opposite the 30∘30^\circ angle, use the sine formula to find the side length xx opposite the 50∘50^\circ angle. Show your working and give your answer correct to 3 significant figures.

  2. 2. A triangle has angles 52∘52^\circ, 63∘63^\circ, and an unknown angle AA. A side of length 6 cm6\ \text{cm} lies opposite angle AA. Find angle AA, then use the sine formula to find the side xx opposite the 63∘63^\circ angle. Give xx correct to 3 significant figures.

  3. 3. In a triangle, one angle is 120∘120^\circ, another is 13∘13^\circ, and the side opposite the 13∘13^\circ angle is 1 cm1\ \text{cm}. Use the sine formula to find the side xx opposite the 120∘120^\circ angle. Give your answer correct to 3 significant figures.

  4. 4. A triangle has angles 46∘46^\circ, 83∘83^\circ, and an unknown angle BB. A side of length 7 cm\sqrt{7}\ \text{cm} lies opposite the 83∘83^\circ angle. Find angle BB, then use the sine formula to find the side xx opposite angle BB. Give xx correct to 3 significant figures.

  5. 5. A triangle has angles 45∘45^\circ, 105∘105^\circ, and an unknown angle AA. A side of length 8 cm\sqrt{8}\ \text{cm} lies opposite angle AA. Find AA, then use the sine formula to find the side xx opposite the 45∘45^\circ angle. Simplify your final answer exactly.

Transcript
## Page 1 S5 Math CP Chapter 9 Applications of Trigonometry in 2-dimensional Problems Name ________________ Class __ ( ) 1 Secondary 5 Mathematics Compulsory Part Chapter 9 Applications of Trigonometry in 2-dimensional Problems Solution Classwork Chapter 9.1 Sine Formula In each of the following triangles, find the value of xx. [Nos. 1–6] 1. ![](https://i.imgur.com/1.png) 2. ![](https://i.imgur.com/2.png) 3. ![](https://i.imgur.com/3.png) 1. By the sine formula, x cmsin⁡50∘=4 cmsin⁡30∘\frac{x \text{ cm}}{\sin 50^\circ} = \frac{4 \text{ cm}}{\sin 30^\circ} x=4sin⁡50∘sin⁡30∘x = \frac{4 \sin 50^\circ}{\sin 30^\circ} =6.13‾, cor. to 3 sig. fig.= \underline{6.13}, \text{ cor. to } 3 \text{ sig. fig.} 2. By the sine formula, x cmsin⁡86∘=6 cmsin⁡60∘\frac{x \text{ cm}}{\sin 86^\circ} = \frac{6 \text{ cm}}{\sin 60^\circ} x=6sin⁡86∘sin⁡60∘x = \frac{6 \sin 86^\circ}{\sin 60^\circ} =6.91‾, cor. to 3 sig. fig.= \underline{6.91}, \text{ cor. to } 3 \text{ sig. fig.} 3. By the sine formula, x cmsin⁡120∘=1 cmsin⁡13∘\frac{x \text{ cm}}{\sin 120^\circ} = \frac{1 \text{ cm}}{\sin 13^\circ} x=sin⁡120∘sin⁡13∘x = \frac{\sin 120^\circ}{\sin 13^\circ} =3.85‾, cor. to 3 sig. fig.= \underline{3.85}, \text{ cor. to } 3 \text{ sig. fig.} 4. ![](https://i.imgur.com/4.png) 5. ![](https://i.imgur.com/5.png) 6. ![](https://i.imgur.com/6.png) 4. A+B+C=180∘A + B + C = 180^\circ A+52∘+63∘=180∘A + 52^\circ + 63^\circ = 180^\circ A=65∘A = 65^\circ By the sine formula, x cmsin⁡63∘=6 cmsin⁡65∘\frac{x \text{ cm}}{\sin 63^\circ} = \frac{6 \text{ cm}}{\sin 65^\circ} x=6sin⁡63∘sin⁡65∘x = \frac{6 \sin 63^\circ}{\sin 65^\circ} =5.90‾, cor. to 3 sig. fig.= \underline{5.90}, \text{ cor. to } 3 \text{ sig. fig.} 5. A+B+C=180∘A + B + C = 180^\circ 46∘+B+83∘=180∘46^\circ + B + 83^\circ = 180^\circ B=51∘B = 51^\circ By the sine formula, x cmsin⁡51∘=7 cmsin⁡83∘\frac{x \text{ cm}}{\sin 51^\circ} = \frac{\sqrt{7} \text{ cm}}{\sin 83^\circ} x=7sin⁡51∘sin⁡83∘x = \frac{\sqrt{7} \sin 51^\circ}{\sin 83^\circ} =2.07‾, cor. to 3 sig. fig.= \underline{2.07}, \text{ cor. to } 3 \text{ sig. fig.} 6. A+B+C=180∘A + B + C = 180^\circ A+45∘+105∘=180∘A + 45^\circ + 105^\circ = 180^\circ A=30∘A = 30^\circ By the sine formula, x cmsin⁡45∘=8 cmsin⁡30∘\frac{x \text{ cm}}{\sin 45^\circ} = \frac{\sqrt{8} \text{ cm}}{\sin 30^\circ} x=8sin⁡45∘sin⁡30∘x = \frac{\sqrt{8} \sin 45^\circ}{\sin 30^\circ} =4‾= \underline{4}