Question

find the smallest angle of δwxy.

Explanation:

Step1: Recall angle - side relationship

In a triangle, the smallest angle is opposite the shortest side.

Step2: Identify the shortest side

The sides of the triangle are 36 km and 114 km. The shortest side is 36 km.

Step3: Determine the angle opposite the shortest side

The angle opposite the 36 - km side is $\angle Y$.
We use the Law of Cosines to find $\angle Y$. The Law of Cosines formula is $w^{2}=x^{2}+y^{2}-2xy\cos W$. First, we can also use the Law of Sines $\frac{\sin Y}{36}=\frac{\sin95^{\circ}}{114}$.
$\sin Y=\frac{36\times\sin95^{\circ}}{114}$
$\sin Y=\frac{36\times0.9962}{114}$
$\sin Y=\frac{35.8632}{114}\approx0.3146$
$Y = \sin^{- 1}(0.3146)\approx18.3^{\circ}$

Answer:

$\angle Y\approx18.3^{\circ}$