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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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.

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

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4:27

Intro to Law of Sines

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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