Use the law of sines to find the indicated part of each triangle ABC.

Find b if a = 165 m, A = 100.2°, B = 25.0°

검증된 단계별 안내

Identify the known values from the problem: side \(a = 165\) m, angle \(A = 100.2^\circ\), and angle \(B = 25.0^\circ\).

Use the fact that the sum of angles in a triangle is \(180^\circ\) to find angle \(C\): calculate \(C = 180^\circ - A - B\).

Write down the Law of Sines formula: \(\frac{a}{\sin A} = \frac{b}{\sin B}\).

Rearrange the 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 \(b\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

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

Law of Sines

The Law of Sines relates the sides and angles of a triangle by stating that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides. It is expressed as (a/sin A) = (b/sin B) = (c/sin C), and is especially useful for solving triangles when two angles and one side or two sides and a non-included angle are known.

Triangle Angle Sum Property

The sum of the interior angles in any triangle is always 180°. This property allows you to find the third angle when two angles are known, which is essential for applying the Law of Sines correctly, as all three angles must be known or determined to solve for unknown sides.

Solving for Unknown Sides

Once the Law of Sines is set up, solving for an unknown side involves rearranging the formula to isolate the desired side length. This requires substituting known values for sides and angles, calculating sine values, and performing algebraic manipulation to find the missing side accurately.

Use the law of sines to find the indicated part of each triangle ABC.Find b if a = 165 m, A = 100.2°, B = 25.0°