In oblique triangle ABC, A = 34°, B = 68°, and a = 4.8. Find b to the nearest tenth.

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Identify the given information: angle A = 34°, angle B = 68°, and side a = 4.8 opposite angle A.

Calculate the third angle C using the triangle angle sum property: \(C = 180^\circ - A - B\).

Use the Law of Sines to relate sides and angles: \(\frac{a}{\sin A} = \frac{b}{\sin B}\).

Rearrange the Law of Sines formula to solve for side b: \(b = \frac{a \cdot \sin B}{\sin A}\).

Substitute the known values of a, A, and B into the formula and prepare to calculate b (do not compute the final value).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Angle Sum Property of a Triangle

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 oblique triangles.

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 in oblique triangles when given some combination of sides and angles.

Rounding and Approximation

When solving trigonometric problems, especially with decimals, rounding to a specified precision (here, the nearest tenth) is important for clarity and practical use. This involves using appropriate significant figures after calculation.

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