a. Use the measurements shown to find a, to the nearest tenth of a foot, in oblique triangle ABC.

Question

SnapAndSolve AI · Accepted Answer

To find side a in triangle ABC, we can use the Law of Sines:

Law of Sines: \( \frac{a}{\sin A} = \frac{b}{\sin B} \)

Given:

First, find angle C:

\( C = 180^\circ - A - B = 180^\circ - 15^\circ - 25^\circ = 140^\circ \)

Now apply the Law of Sines:

\( \frac{a}{\sin 15^\circ} = \frac{450}{\sin 25^\circ} \)

\( a = \frac{450 \times \sin 15^\circ}{\sin 25^\circ} \)

Using a calculator:

\( a \approx \frac{450 \times 0.2588}{0.4226} \approx 275.0 \text{ feet} \)

Therefore, \( a \approx 275.0 \text{ feet} \).

Answer