Question

find the smallest angle of $\triangle tuv$.

Explanation:

Step1: Identify shortest side

The shortest side is $TV = 16$ m, opposite $\angle U$.

Step2: Apply Law of Cosines

Law of Cosines: $\cos U = \frac{TU^2 + UV^2 - TV^2}{2 \cdot TU \cdot UV}$
Substitute values: $\cos U = \frac{25^2 + 26^2 - 16^2}{2 \cdot 25 \cdot 26}$

Step3: Calculate numerator/denominator

Numerator: $625 + 676 - 256 = 1045$
Denominator: $2 \cdot 25 \cdot 26 = 1300$
$\cos U = \frac{1045}{1300} = 0.8038$

Step4: Find angle U

$\angle U = \cos^{-1}(0.8038) \approx 36.4^\circ$

Answer:

$\approx 36.4^\circ$ (or $\angle U$)