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Angles ∝ and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β if β > ∝. sin( x/2 + 20) = cos(2x - 25/2 )

A)
25°


B)
33°


C)
36.5°

D)
53.5°

Respuesta :

The answer is D: 53.5
issaspammingmoodfam

53.5°

Sine and cosine of complementary angles. Thus,

[tex](\frac{x}{2} + 20 ) + (2x - \frac{25}{2}) = 90[/tex]

[tex]x = 33[/tex]

then,

[tex]\frac{33}{2} + 20[/tex]  → [tex]x= 36.5[/tex]

[tex]2(33) - \frac{25}{2}[/tex]  →  [tex]x = 53.5[/tex]

thus,

β [tex]= 53.5[/tex]

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