Image_20261104204427_154_128.jpg

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

1. In a triangle with angles $30^\circ$ , $45^\circ$ , and $105^\circ$ , the side opposite the $30^\circ$ angle has length 6. Use the sine formula to find the length of the side opposite the $45^\circ$ angle.
2. Explain why the sine formula cannot be directly used to find an unknown side when only the three angles of a triangle are given.
3. A triangle has angles $30^\circ$ , $x^\circ$ , and $100^\circ$ . Write an expression for the ratio of the side opposite $x^\circ$ to the side opposite $30^\circ$ , using the sine formula.
4. In a triangle, side $a = 10$ lies opposite angle $A = 30^\circ$ , and side $b$ lies opposite angle $B = 45^\circ$ . Without calculating, explain how you would use the sine formula to compare $a$ and $b$ .
5. A student writes: 'In any triangle, $\frac{a}{A} = \frac{b}{B} = \frac{c}{C}$ , where $a,b,c$ are sides and $A,B,C$ are opposite angles in degrees.' Explain why this is incorrect, and give the correct relationship.

Transcript

## Page 1 Secondary 5 Mathematics Compulsory Part Chapter 9 Applications of Trigonometry in 2-dimensional Problems Classwork Chapter 9.1 Sine Formula In each of the following triangles, find the value of

x

. [Nos. 1–6] 1.

C

\quad\quad\quad\quad\quad\quad30^\circ

$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\