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slavikrds [6]
3 years ago
12

HELP IS FOR TODAY GIVE ME THE ANSWER AND HOW TO DO IT

Mathematics
1 answer:
raketka [301]3 years ago
7 0

Answer:

Part 1)

a) sin(A)=\frac{9}{41}

b) sin(B)=\frac{40}{41}

c) cos(A)=\frac{40}{41}

d) cos(B)=\frac{9}{41}

e) tan(A)=\frac{9}{40}

f) tan(B)=\frac{40}{9}

Part 2) x=9.4\ units (see the explanation)

Part 3) x=12.5\ units (see the explanation)

Part 4) x=4.5\ units (see the explanation)

Part 5) x=41.8^o (see the explanation)

Part 6) x=50.2^o (see the explanation)

Part 7) x=56.9^o (see the explanation)

Step-by-step explanation:

Part 1)

step 1

Find sin(A)

we know that

sin(A)=\frac{BC}{AB} ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

sin(A)=\frac{9}{41}

step 2

Find sin(B)

we know that

sin(B)=\frac{AC}{AB} ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

sin(B)=\frac{40}{41}

step 3

Find cos(A)

we know that

If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa

In this problem

Angle A and Angle B are complementary

so

cos(A)=sin(B)  ----> by complementary angles

therefore

cos(A)=\frac{40}{41}

step 4

Find cos(B)

we know that

If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa

In this problem

Angle A and Angle B are complementary

so

cos(B)=sin(A)  ----> by complementary angles

therefore

cos(B)=\frac{9}{41}

step 5

Find tan(A)

we know that

tan(A)=\frac{BC}{AC} ----> by TOA (opposite side divided by adjacent side)

substitute the given values

tan(A)=\frac{9}{40}

step 6

Find tan(B)

we know that

tan(B)=\frac{AC}{BC} ----> by TOA (opposite side divided by adjacent side)

substitute the given values

tan(B)=\frac{40}{9}

Part 2) we know that

tan(58^o)=\frac{15}{x} ----> by TOA (opposite side divided by adjacent side)

solve for x

x=\frac{15}{tan(58^o)}

x=9.4\ units

Part 3) we know that

sin(53^o)=\frac{10}{x} ----> by SOH (opposite side divided by the hypotenuse)

solve for x

x=\frac{10}{sin(53^o)}

x=12.5\ units

Part 4) we know that

cos(41^o)=\frac{x}{6} ----> by CAH (adjacent side divided by the hypotenuse)

solve for x

x=(6)cos(41^o)

x=4.5\ units

Part 5) we know that

sin(x)=\frac{4}{6} ----> by SOH (opposite side divided by the hypotenuse)

solve for angle x

x=sin^{-1}(\frac{4}{6})

x=41.8^o

Part 6) we know that

tan(x)=\frac{30}{25} ----> by TOA (opposite side divided by adjacent side)

solve for angle x

x=tan^{-1}(\frac{30}{25})

x=50.2^o

Part 7) we know that

cos(x)=\frac{12}{22} ----> by CAH (adjacent side divided by the hypotenuse)

solve for angle x

x=cos^{-1}(\frac{12}{22})

x=56.9^o

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