Pass Check: Trigonometry
SOH CAH TOA for right triangles; sine and cosine rules for any triangle.
Opposite, adjacent, hypotenuse
The three sides of a right triangle relative to the angle being used: opposite is across from it, adjacent is next to it, hypotenuse is the longest side.
Sine rule
Relates sides and angles in any triangle: a/sin A = b/sin B = c/sin C.
Cosine rule
Finds a side or angle in any triangle when SOH CAH TOA cannot be used (no right angle).
Angle of elevation/depression
The angle up from horizontal to an object above (elevation) or down to an object below (depression).
Quick check
Mixed quiz
1. A right-angled triangle has opposite side 11 cm and adjacent side 13 cm. Find the angle, to 1 decimal place.
2. In a right-angled triangle the hypotenuse is 10 cm and one angle is 30 degrees. Find the length of the side opposite this angle, to 1 decimal place.
3. Which ratio connects adjacent and hypotenuse?
4. A right-angled triangle has opposite side 6 cm and adjacent side 8 cm. Find the angle, to 1 decimal place.
5. In a right-angled triangle the hypotenuse is 10 cm and one angle is 45 degrees. Find the length of the side opposite this angle, to 1 decimal place.
6. A right-angled triangle has opposite side 8 cm and adjacent side 10 cm. Find the angle, to 1 decimal place.
7. Which ratio should be used to find an angle when you know the opposite and hypotenuse?
8. A right-angled triangle has opposite side 10 cm and adjacent side 12 cm. Find the angle, to 1 decimal place.