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Solve the right triangle. Give angles in degrees and minutes.
A = 33.3◦; b = 3.8m Round side lengths to one decimal place.

A) B = 56.7◦; a = 2.5mc = 4.5m
B) B = 56.7◦; a = 5.0mc = 6.3m
C) B = 56.7◦; a = 1.4mc = 4.0m
D) B = 56.7◦; a = 1.4mc = 5.0m
E) none of the above

*Can you please tell me which one is the right choice, and how did you get that choice?

*Can you explain what is (mc) and how to convert it to (m)?

Solve the right triangle Give angles in degrees and minutesA 333 b 38m Round side lengths to one decimal placeA B 567 a 25mc 45mB B 567 a 50mc 63mC B 567 a 14mc class=

Respuesta :

calculista

Answer:

Option A

[tex]m\angle B=56.7^o[/tex]

[tex]a=2.5\ m[/tex]

[tex]c=4.5\ m[/tex]

Step-by-step explanation:

step 1

Find the measure of angle B

we know that

[tex]m\angle A+m\angle B=90^o[/tex] ----> by complementary angles

we have

[tex]m\angle A=33.3^o[/tex]

substitute

[tex]33.3^o+m\angle B=90^o[/tex]

[tex]m\angle B=90^o-33.3^o[/tex]

[tex]m\angle B=56.7^o[/tex]

step 2

Find the measure of side c

Applying the law of sines

[tex]\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

we have

[tex]b=3.8\ m\\B=56.7^o\\C=90^o[/tex]

substitute

[tex]\frac{3.8}{sin(56.7^o)}=\frac{c}{sin(90^o)}[/tex]

[tex]c=\frac{3.8}{sin(56.7^o)}sin(90^o)[/tex]

[tex]c=4.5\ m[/tex]

step 3

Find the measure of side a

Applying the law of sines

[tex]\frac{b}{sin(B)}=\frac{a}{sin(A)}[/tex]

we have

[tex]b=3.8\ m\\B=56.7^o\\A=33.3^o[/tex]

substitute

[tex]\frac{3.8}{sin(56.7^o)}=\frac{a}{sin(33.3^o)}[/tex]

[tex]a=\frac{3.8}{sin(56.7^o)}sin(33.3^o)[/tex]

[tex]a=2.5\ m[/tex]

Note: (mc) is not a unit, in the question the options were written without leaving any space

so

B = 56.7◦; a = 2.5mc = 4.5m

instead of

B = 56.7◦; a = 2.5 m; c=4.5 m

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