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In right triangle ABC with the right angle at C, sin A= 2x + .1 and cos B = 4x - .7. Determine and state the vaule of x.

Sagot :

RedRicin
Imagine [tex]\angle A[/tex] at the top of the triangle and [tex]\angle B[/tex] at the bottom. (or used the attached picture for reference)

[tex]\sin A= \frac{opposite}{hypotenuse}[/tex]

[tex]\cos B = \frac{adjacent}{hypotenuse}[/tex]

One thing to note, however, is that the side opposite [tex]\angle A[/tex] is the same side as the one adjacent to [tex]\angle B[/tex]! Thus [tex]\sin A=\cos B[/tex].

Substitute these values for [tex]2x+0.1[/tex] and [tex]4x-0.7[/tex] and solve.

 [tex]4x-0.7=2x+0.1 \\ 4x=2x+0.8 \\ 2x=0.8\\ \boxed{x=0.4}[/tex]
View image RedRicin
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