Solve each triangle ABC.
A = 68.41°, B = 54.23°, a = 12.75 ft

검증된 단계별 안내

Identify the given information: angle A = 68.41°, angle B = 54.23°, and side a = 12.75 ft. Since two angles and one side are given, this is an ASA (Angle-Side-Angle) case.

Find the third angle C using the fact that the sum of angles in a triangle is 180°. Use the formula: \(C = 180^\circ - A - B\).

Use the Law of Sines to find side b. The Law of Sines states: \(\frac{a}{\sin A} = \frac{b}{\sin B}\). Rearrange to solve for \(b\): \(b = \frac{a \sin B}{\sin A}\).

Similarly, use the Law of Sines to find side c: \(\frac{a}{\sin A} = \frac{c}{\sin C}\), so \(c = \frac{a \sin C}{\sin A}\).

After calculating sides b and c, summarize the triangle with all sides and angles known.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Triangle Angle Sum Property

The sum of the interior angles in any triangle is always 180°. Knowing two angles allows you to find the third by subtracting their sum from 180°, which is essential for solving the triangle completely.

Law of Sines

The Law of Sines relates the sides and angles of a triangle: (a/sin A) = (b/sin B) = (c/sin C). It is used to find unknown sides or angles when given some combination of sides and angles, especially in non-right triangles.

Solving Triangles

Solving a triangle means finding all unknown sides and angles. Using known angles and sides, along with the Law of Sines and angle sum property, you can systematically determine all missing measurements.

Solve each triangle ABC.A = 68.41°, B = 54.23°, a = 12.75 ft