Solve each right triangle. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2.

검증된 단계별 안내

Identify the given sides of the right triangle. Label the sides as opposite (O), adjacent (A), and hypotenuse (H) relative to the angle you want to find.

Use the Pythagorean theorem \(H^2 = O^2 + A^2\) to find the missing side if only two sides are given and the hypotenuse is not one of them.

Apply the appropriate trigonometric ratio to find the unknown angles. For example, use \(\sin \theta = \frac{O}{H}\), \(\cos \theta = \frac{A}{H}\), or \(\tan \theta = \frac{O}{A}\) depending on the sides you have.

Calculate the angle in degrees using the inverse trigonometric function, such as \(\theta = \sin^{-1}\left(\frac{O}{H}\right)\), \(\theta = \cos^{-1}\left(\frac{A}{H}\right)\), or \(\theta = \tan^{-1}\left(\frac{O}{A}\right)\).

Convert the decimal degrees to degrees and minutes by separating the integer part as degrees and multiplying the decimal part by 60 to get minutes.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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

Pythagorean Theorem

The Pythagorean theorem relates the lengths of the sides in a right triangle: the square of the hypotenuse equals the sum of the squares of the other two sides. It is essential for finding the missing side when two sides are known.

Trigonometric Ratios (Sine, Cosine, Tangent)

Sine, cosine, and tangent ratios connect the angles of a right triangle to the ratios of its sides. These ratios allow calculation of unknown angles or sides when two sides are given, using inverse trigonometric functions for angle determination.

Angle Measurement in Degrees and Minutes

Angles can be expressed in degrees and minutes, where one degree equals 60 minutes. Converting decimal degrees to degrees and minutes is important for precise angle representation, especially in practical applications like navigation or surveying.