For the angles and in the figures find cos 6 4 Solutionc

For the angles ? and ? in the figures, find

cos(? + ?).

Solution

cos( + ) = cos cos - sin sin

from triangle 1

cos = base / hypotenuse

hypotenuse = sqrt ( 4^2 + 1^2 ) = sqrt 17

cos = 4 / sqrt 17

sin = 1 / sqrt 17

from triangle 2

cos = sqrt ( 36 - 16 )/ 6 = sqrt 20 / 6

sin = 4 / 6 = 2 / 3

plugging the values in the formula

cos( + ) = cos cos - sin sin = 4 / sqrt 17 * sqrt 20 / 6 - 1 / sqrt 17 * 2/3

= (4 sqrt 5 - 2 )/ 3 sqrt 17 or   ( 4 sqrt 85 - 2 sqrt 17 ) / 51