First, we work out the final angle of the left triangle, which has a total of 180°. To do this we take 40° and 66° from 180°, giving us <u>72°</u>
Because there is a straight line along the bottom (which will total 180°), we take both 72° and 56° from 180°, giving us <u>52°</u>, which is the bottom left angle of the right triangle.
Finally, to work out '?', we take 52° and 40° from 180° to get our final answer of <u>88°.</u>
The values of sin θ and cos θ represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos θ finds the unknown leg, and then all other trigonometric values can be found.
