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100 POINTS AND BRAINLIEST!! PRE CALC

Given the sign x = 3/5, sin y = 7/25, and x and y are both acute angles, the value of tan (x - y) is

a. 39/32
b. 44/117
c. 44/7
d. 4/3

Please explain your answer :)

Answer :

Answer:

B

Step-by-step explanation:

sinx = 3/5

to find the value of x...figure sine inverse(Arcsin) of 3/5 out.

sin^-1 ( 3/5) = 0.64.

siny = 7/25

sin^-1(7/25) = 0.28

x = 0.64

y = 0.28

tan(x-y)

=tan(0.64-0.28)

= tan (0.36)

= tan (9/25)

= 0.376.

now divide every fraction given from a - d to find the one equivalent to 0.376 because that's the value of tan(x-y).

B. 44 / 117 = 0.376.

Answer:

b

Step-by-step explanation:

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex]

This is a 3- 4- 5 right triangle

with adjacent side = 4 , then

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex] , thus

tan x = [tex]\frac{sinx}{cosx}[/tex] = [tex]\frac{\frac{3}{5} }{\frac{4}{5} }[/tex] = [tex]\frac{3}{5}[/tex] × [tex]\frac{5}{4}[/tex] = [tex]\frac{3}{4}[/tex]

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sin y = [tex]\frac{7}{25}[/tex]

This is a 7- 24- 25 right triangle

with adjacent side = 24 , then

cos y = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{24}{25}[/tex] , thus

tan y = [tex]\frac{siny}{cosy}[/tex] = [tex]\frac{\frac{7}{25} }{\frac{24}{25} }[/tex] = [tex]\frac{7}{25}[/tex] × [tex]\frac{25}{24}[/tex] = [tex]\frac{7}{24}[/tex]

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tan(x - y) = [tex]\frac{tanx-tany}{1+tanxtany}[/tex]

             = [tex]\frac{\frac{3}{4}-\frac{7}{24} }{1+\frac{3}{4}(\frac{7}{24}) }[/tex]

             = [tex]\frac{\frac{11}{24} }{1+\frac{21}{96} }[/tex]

             = [tex]\frac{\frac{11}{24} }{\frac{117}{96} }[/tex]

             = [tex]\frac{11}{24}[/tex] × [tex]\frac{96}{117}[/tex]

             = [tex]\frac{11}{1}[/tex] × [tex]\frac{4}{117}[/tex]

             = [tex]\frac{44}{117}[/tex] → b