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S.2 Mathematics Chapter 11 Trigonometric Ratio Worksheet for Section 11.1 Sine Ratio Worksheet 1: Right-angled triangle with a given acute angle 30o The figure below shows a right-angled triangle ABC, where B = and C = 90. Part 1 Measure the length of the opposite sides and the hypotenuses by a ruler for the following right-angled triangles with a given acute angle 30o of different size. Calculate their ratio and complete the following table. Example 1. 2. N E B A C 3. F D 4. Q O M 5. S T P Y X Z R U Example opposite side (cm) hypotenuse (cm) 1 2 Ratio of opposite side to hypotenuse (Answer in decimal number) 1 0.5 2 1. 2. 3. 4. 5. S.2 Mathematics Chapter 11 Trigonometric Ratios (Section 1 The Sine Ratio) Worksheet Page 1 Part 2 From the data obtained from the table above, we have: For all right-angled triangles having the same acute angle 30o, their ratios of the opposite side to the hypotenuse are equal to __________, regardless of the sizes of the triangle. i.e. opposite side for 30o ______ hypotenuse Part 3 Let’s Think 1. For a right-angled triangle with a given acute angle 30o, Can you find the following values without measurement by ruler? (a) Length of the opposite side □ Yes, Answer = __________ □ No (b) Length of the hypotenuse □ Yes, Answer = __________ □ No (c) Ratio of the opposite side to the hypotenuse □ Yes, Answer = __________ □ No 2. From the result obtained from Part 2, is it true for all right-angled triangles with different acute angles? □ Yes or □ No Worksheet 2: The Ratio of the opposite side to the hypotenuse for different acute angles (Sine Ratio) Part 1 A right-angled triangle will be shown on the screen. We drag the red point on the right hand side to change the size of the right-angled triangle. And then we drag the green point on the left hand side to change the angles of the right-angled triangle. Drag the red point to change the size of the right-angled triangle. Drag the green point to change the angles of the right-angled triangle. opposite side = 0.5 hypotenuse = 1 the ratio = 0.5 Part 2 The ratio of the opposite side to the hypotenuse for different angles will be shown on the screen. Complete the following table. opposite side hypotenuse 5o 10o 15o 20o 25 o 30 o 35 o 40 o opposite side hypotenuse 45o 50o 55o 60o 65 o 70 o 75 o 80 o S.2 Mathematics Chapter 11 Trigonometric Ratios (Section 1 The Sine Ratio) Worksheet Page 2 Part 3 From the data obtained from the table in Part 2, we have the following observation. 1. 2. opposite side will hypotenuse opposite side When 0o < < 90o, the ratio of lies between hypotenuse When increases, the ratio of . and . Part 4 By using the table in Part 2, find the unknown in each of the following right-angled triangles. (Give the answer correct to 1 decimal place.) Example: Solution: x 0.5 4 x = 0.54 = 2 4. 1. 5. 2. 6. 12.7 12.5 3. Let us think: 1. 2. S.2 Mathematics Chapter 11 Trigonometric Ratios (Section 1 The Sine Ratio) Worksheet Page 3 Worksheet 3: Calculator and the Sine Ratio For any right-angled triangle, Part 3 Use a calculator to find the unknown in each of the following right-angled triangles. (Give the answer correct to 3 significant figures.) Example: The ratio of the opposite side to the hypotenuse for a given acute angle is called the sine ratio of . It is denoted by sin and opposite side sin hypotenuse Part 1 By using a calculator, find the following value. angle (2 d.p.) 5° 15 0.2 x 43o 1. x = 15sin43o x = 10.2 10.5 78o sin (i.e. sine ratio) (4 d.p.) 20° 23° Solution: x sin 43o 15 y 2. 0.6 0.8 61° 0.9 0.95 82° 2 If the value of sin is given, we can find out the acute angle by a calculator. 1. Set the calculator to degree mode first. 2. Press the SHIFT and sin keys, then enter the sine ratio. 3. Press the EXE key. 1 If the value of angle is given, we can find out the sine ratio of a given angle (i.e. sin ). 1. Set the calculator to degree mode first. 2. Press the sin key and enter the angle. 3. Press the EXE key. 3. Part 2 Do the following questions on your C.W. book. 1. 2. 3. 4. 5. By using a calculator, find the values of the following expressions correct to 4 significant figures. (a) sin 43 – sin 28 (b) 2 sin 11 By using a calculator, find the values of the following expressions correct to 4 decimal places. (a) sin 66 (b) sin 32.48 (a) By using a calculator, find the value of sin 34 + sin 26 sin 60 correct to 3 significant figures. (b) From the result obtained in (a), is sin 34 + sin 26 equal to sin (34 + 26)? Find the acute angle in each of the following using a calculator. (Give your answers correct to 3 significant figures.) (a) sin = 0.22 (b) sin = sin 68 – sin 40 Find the acute angles in the following using a calculator. (a) sin 0.62, correct to the nearest degree. (b) sin =(1/5) sin 35, corr. to the nearest 0.1. (c) 7 sin = 3, corr. to 3 significant figures. 4. 5. Part 4 Do Ex.11A Q.13-18 (P.180) on your C.W. book. S.2 Mathematics Chapter 11 Trigonometric Ratios (Section 1 The Sine Ratio) Worksheet Page 4