Answer:
x = 35°
Step-by-step explanation:
From the question given above:
cos x = sin(20 + x)
The value of x can be obtained as follow:
cos x = sin(20 + x)
Recall:
sin(A + B) = sinAcosB + cosAsinB
Therefore,
sin(20 + x) = sin20cosx + cos20sinx
cos x = sin(20 + x)
cos x = sin20cosx + cos20sinx
Collect like terms
cos x – sin20cosx = cos20sinx
cos x(1 – sin20) = cos20sinx
Divide both side by cosx
(1 – sin20) = cos20sinx / cosx
Recall:
Tan x = sinx / cosx
(1 – sin20) = cos20tanx
Divide both side by cos20
(1 – sin20) / cos20 = tanx
(1 – 0.3420) / 0.9397 = tanx
0.658 / 0.9397 = tanx
0.7 = tanx
Take the inverse of tan
x = tan¯ 0.7
x = 35°
