Worksheet Chapter 5: Trigonometric Ratios

1. Which of the following is equivalent to sin 70°?

2. True or False: The value of tan 45° is equal to 1.

3. In triangle ABC, ∠B = 90°. Given that tan ∠BAC = 43 and AB = 9 cm. Calculate: (a) The length of side BC. (b) The length of side AC. (c) The value of sin ∠BAC.

4. Fill in the blank: The trigonometric ratio represented by the fraction (Opposite / Hypotenuse) is ________.

5. In a right-angled triangle XYZ, ∠Y = 90°, XY = 5 cm, and YZ = 12 cm. Find the value of cos ∠YZX.

6. Convert the angle 54.45° into degrees and minutes.

7. True or False: For any acute angle θ, sin θ can be greater than 1.

8. Evaluate the exact expression: 2(sin 30°) + 4(cos 60°) - tan 45°.

9. A ramp length of 10 m is inclined at an angle of 28° to the horizontal ground. Calculate: (a) The vertical height raised by the ramp. (b) The horizontal distance covered by the ramp. (Give answers correct to 2 decimal places).

10. A surveyor stands 50 m away from the base of a tall building. Looking up to the top of the building, the angle of elevation measured is 38°. If the surveyor's eye level is 1.6 m above the ground, calculate the total height of the building in metres (to 2 decimal places).