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4 votes
If sinA = cosB, what is the relationship between A and B if A is obuse angled and B is acute angled ?

User Argaen
by
7.6k points

1 Answer

5 votes

Answer:

According to the law of sines, \dfrac{AB}{\sin(\angle C)}=\dfrac{AC}{\sin(\angle B)}

sin(∠C)

AB

=

sin(∠B)

AC

start fraction, A, B, divided by, sine, left parenthesis, angle, C, right parenthesis, end fraction, equals, start fraction, A, C, divided by, sine, left parenthesis, angle, B, right parenthesis, end fraction. Now we can plug the values and solve:

\begin{aligned} \dfrac{AB}{\sin(\angle C)}&=\dfrac{AC}{\sin(\angle B)} \\\\ \dfrac{5}{\sin(33^\circ)}&=\dfrac{AC}{\sin(67^\circ)}\\\\ \dfrac{5\sin(67^\circ)}{\sin(33^\circ)}&=AC \\\\ 8.45&\approx AC \end{aligned}

sin(∠C)

AB

sin(33

)

5

sin(33

)

5sin(67

)

8.45

=

sin(∠B)

AC

=

sin(67

)

AC

=AC

≈AC

User Vpv
by
8.0k points
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