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

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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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Concetti chiave

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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.

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4:47

Sum and Difference of Tangent

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.

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Intro to Law of Sines

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.

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