Foundations & Precalculus 10
Worksheet (Sine & cosine ratios)
YOU MUST SHOW YOUR WORK WHENEVER POSSIBLE!
1. Determine the sine and cosine of each angle to the nearest hundredth.
a) 57°
b) 5°
c) 19°
d) 81°
2. To the nearest degree, determine the measure of each X .
a) sin X  0.25
c) sin X 
6
11
b) cos X  0.64
d) cos X 
7
9
3. a) In each triangle below:
 name the side opposite ∠A
 name the side adjacent to ∠A
 name the hypotenuse
b) For each triangle, determine sin A and cos A to the nearest hundredth.
i)
ii)
4. Determine the measure of each indicated angle to the nearest degree.
a)
b)
c)
d)
5. Use the sine or cosine ratio to determine the measure of each acute angle to the nearest tenth of a degree.
HINT: Use trigonometry to come up with both answers.
a)
b)
6. Suppose the railroad track through the spiral tunnels from Field to Hector were straightened out. It would
look like the diagram below. The diagram is not drawn to scale. What is the angle of inclination of the track
to the nearest tenth of a degree?
7. A ladder is 6.5 m long. It leans against a wall. The base of the ladder is 1.2 m from the wall. What is the
angle of inclination of the ladder to the nearest tenth of a degree? HINT: Draw a sketch.
8. Sketch a right isosceles triangle. Explain why the cosine of each acute angle is equal to the sine of the
angle.