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A is an acute angle in a right triangle, Given that Sin A= 7/25, what is the ratio for Cos A? Enter your answer in the box as a fraction in simplest form.

A is an acute angle in a right triangle Given that Sin A 725 what is the ratio for Cos A Enter your answer in the box as a fraction in simplest form class=

Respuesta :

Find the adjacent side of the triangle ... 
7² + x² = 25²
x² = 25² - 7²
x² = 576
x = 24 
The adjacent side of the triangle is 24

Given that sin A = [tex] \frac{7}{25} [/tex]
Since sin A = [tex] \frac{o}{h} [/tex]
We can conclude that o = 7 and h = 25

cos A = [tex] \frac{a}{h} [/tex]
cos A = [tex] \frac{24}{25} [/tex]
mathstudent55
[tex] \sin \theta = \dfrac{opp}{hyp} [/tex]

[tex] \sin A = \dfrac{7}{25} = \dfrac{opp}{hyp} [/tex]

[tex] a^2 + b^2 = c^2 [/tex]

[tex] a^2 + 7^2 = 25^2 [/tex]

[tex] a^2 = 625 - 49 [/tex]

[tex] a = \sqrt{576} [/tex]

[tex] a = 24 [/tex]

[tex] adj = a = 24 [/tex]

[tex] \cos A = \dfrac{adj}{hyp} [/tex]

[tex] \cos A = \dfrac{24}{25} [/tex]

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