← Math

Image_20261104204427_155_128.jpg

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

  1. 1. In triangle ABC, angle A = 40°, side b = 7 cm (i.e., AC = 7 cm), and side a = 5 cm (i.e., BC = 5 cm). Use the sine formula to find all possible values of angle B. Explain why there are two possible values.

  2. 2. In triangle ABC, angle A = 40°, side b = 7 cm, and side a = 10 cm. Show that only one value of angle B is possible, and find it correct to 3 significant figures.

  3. 3. In triangle ABC, angle A = 120°, side b = 9 cm, and side a = 15 cm. Find angle B and angle C, and then find side c, all correct to 3 significant figures.

  4. 4. In triangle ABC, angle A = 120°, side b = 9 cm, and side a = 535\sqrt{3} cm. Explain why no triangle can be formed with these measurements.

  5. 5. In triangle ABC, angle B = 30° and side AB = 20 cm. Kelvin says the shortest possible length of side AC is 10 cm. Verify his claim using trigonometry and explain why this is the minimum.

Transcript
## Page 1 S5 Math CP Chapter 9 Applications of Trigonometry in 2-dimensional Problems Name ______________________ Class ________ 4 7. In △ABC\triangle ABC, B=30∘B = 30^\circ and AB=20AB = 20 cm. Explain (a) Kelvin claims that the minimum length of ACAC is 10 cm. Do you agree? Explain your answer. (b) Find the range of the length of ACAC such that two triangles can be formed. (a) sin⁡30∘=AC20\sin 30^\circ = \frac{AC}{20} AC=10AC = 10 cm ∴\therefore Yes (b) 10 cm<AC<20 cm10\text{ cm} < AC < 20\text{ cm} **Supplementary Example 4** Level 2 (P.9.8) In each of the following, use the sine formula to find BB in △ABC\triangle ABC. (a) A=40∘A = 40^\circ, b=7b = 7 cm, a=5a = 5 cm (b) A=40∘A = 40^\circ, b=7b = 7 cm, a=10a = 10 cm (Give the answers correct to 3 significant figures.) (a) 7sin⁡B=5sin⁡40∘\frac{7}{\sin B} = \frac{5}{\sin 40^\circ} B=64.1∘B = 64.1^\circ or 116∘116^\circ (b) 7sin⁡B=10sin⁡40∘\frac{7}{\sin B} = \frac{10}{\sin 40^\circ} B=26.7∘B = 26.7^\circ **Supplementary Example 5** Level 2 (P.9.9) Solve △ABC\triangle ABC in each of the following. (a) A=120∘A = 120^\circ, b=9b = 9 cm, a=15a = 15 cm (b) A=120∘A = 120^\circ, b=9b = 9 cm, a=53a = 5\sqrt{3} cm (Give the answers correct to 3 significant figures.) (a) 9sin⁡B=15sin⁡120∘\frac{9}{\sin B} = \frac{15}{\sin 120^\circ} B=31.3∘B = 31.3^\circ (+120∘+31.3∘=180∘)(+120^\circ + 31.3^\circ = 180^\circ) C=28.7∘C = 28.7^\circ csin⁡28.7∘=15sin⁡120∘\frac{c}{\sin 28.7^\circ} = \frac{15}{\sin 120^\circ} c=8.32c = 8.32 (b) 9sin⁡B=53sin⁡120∘\frac{9}{\sin B} = \frac{5\sqrt{3}}{\sin 120^\circ} B=64.2∘B = 64.2^\circ A+B=120∘+64.2∘A + B = 120^\circ + 64.2^\circ =184.2∘= 184.2^\circ >180∘> 180^\circ ∴\therefore No solution