Answer:
[tex] \frac{20}{29} [/tex]
Step-by-step explanation:
Let x replace theta.
Apply pythagorean trig identity
[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]
[tex] (\frac{21}{29} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]
[tex] \frac{441}{841} + \cos {}^{2} (x) = 1[/tex]
[tex] \cos {}^{2} (x) = 1 - \frac{441}{841} [/tex]
[tex] \cos {}^{2} (x) = \frac{400}{841} [/tex]
[tex] \cos(x) = \frac{20}{29} [/tex]
Cosine is positve in 1st quadrant so the answer is
[tex] \frac{20}{29} [/tex]
