In ΔIJK, k = 730 inches, j = 700 inches and ∠J=44°. Find all possible values of ∠K, to the nearest degree. I
J
K
j = 700
k = 730
44°
?°
\frac{\sin A}{a}=\frac{\sin B}{b}
a
sinA
​
=
b
sinB
​

From the reference sheet (reciprocal version).
\frac{\sin K}{730}=\frac{\sin 44}{700}
730
sinK
​
=
700
sin44
​

Plug in values.
\sin K=\frac{730\sin 44}{700}\approx 0.7244294
sinK=
700
730sin44
​
≈0.7244294
Evaluate.
K=\sin^{-1}(0.7244294)\approx 46.42\approx 46^{\circ}
K=sin
−1
(0.7244294)≈46.42≈46
∘

Inverse sine and round.
\text{Quadrant II: } 180-46=134^{\circ}
Quadrant II: 180−46=134
∘

Sine is positive in quadrants 1 and 2.
\text{Check for possibility:}
Check for possibility:
No triangle's angles may add to more than 180.
44+46=90^{\circ}\leftarrow \text{Possible}
44+46=90
∘
←Possible
Less than 180.
44+134=178^{\circ}\leftarrow \text{Possible}
44+134=178
∘
←Possible
Less than 180.
\text{ }46^{\circ}\text{ and } 134^{\circ}

!!!
46
and 134
!!!
yw-Delta math