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

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

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

c

step-by-step explanation: