Math Snap

STEP 1

1. The triangle is a non-right triangle.
2. We will use the Law of Sines to find the missing angle $\theta$.
3. The sum of angles in a triangle is $180^\circ$.

STEP 2

1. Apply the Law of Sines to find angle $B$.
2. Use the sum of angles in a triangle to find the missing angle $\theta$.

STEP 3

Apply the Law of Sines:
$$\frac{\sin A}{BC} = \frac{\sin B}{AC}$$ Substitute the known values:
$$\frac{\sin 88^\circ}{26} = \frac{\sin B}{16.1}$$

STEP 4

Solve for $\sin B$:
$$\sin B = \frac{16.1 \cdot \sin 88^\circ}{26}$$ Calculate $\sin B$:
$$\sin B \approx \frac{16.1 \cdot 0.9998}{26} \approx 0.619$$

STEP 5

Find angle $B$ using the inverse sine function:
$$B = \sin^{-1}(0.619) \approx 38.2^\circ$$

STEP 6

Use the sum of angles in a triangle to find $\theta$:
$$A + B + \theta = 180^\circ$$ Substitute the known angles:
$$88^\circ + 38.2^\circ + \theta = 180^\circ$$

Solve for $\theta$:
$$\theta = 180^\circ - 88^\circ - 38.2^\circ = 53.8^\circ$$ The measure of the missing angle $\theta$ is:
$$\boxed{53.8^\circ}$$