1. Use your calculator to find the sin, cos or tan of the following angles. Give your answers correct to four decimal places where necessary. (i) sin 24° (ii) cos 45°
(iii) tan 88° (iv) tan 12°
(v) sin 43° (vi) cos 79°
(iii) tan C = 0·1405 (iv) cos B = 0·5000
(vii) sin 62° (viii) sin 14°
(ix) cos 60° (x) tan 72°
(v) sin A = 0·4540 (vi) tan B = 0·6249
2. Find the measure of the angle in each of the following. Give your answer to the nearest degree. (i) sin X = 0·7547 (ii) cos Y = 0·5736
3. (a) Use your calculator to find the value of: (i) sin 10° and cos 80° (ii) sin 20° and cos 70° (iii) sin 30° and cos 60°
(b) Using the pattern shown in (a), or otherwise fill in the missing angle below. sin 40° and cos
(xi) cos 31° (xii) tan 25°
(vii) cosW = 0·6157 (viii) tan Z = 19·0811
34.4 Finding missing sides and angles
To find the length of a side
If we are given an angle and one side of the right-angled triangle, we can use sin, cos and tan to find the other sides.
Finding a missing side in a right-angled triangle Label the sides of the triangle: hypotenuse opposite and adjacent. Write down the measure of the angle we ‘have’ (given in the question). Write down the name of the side we ‘have’ (given in the question). Write down the name of the side we ‘want’ (asked to find in the question). Decide which ratio to use depending on the sides identified in steps 2–4. Form an equation with the angle given and the sides identified in steps 2–4. Solve the equation to find the unknown side.
1
2 3 4 5 6 7
By the end of this section you should be able to: ● use sin, cos and tan to find missing sides ● use sin, cos and tan to find missing angles