Find the length of the remaining side of each triangle. Do not use a calculator.

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검증된 단계별 안내

Identify the type of triangle and the given sides or angles from the image. Typically, you will have either a right triangle or a non-right triangle with some sides and angles labeled.

If the triangle is a right triangle, use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs. Rearrange the formula to solve for the missing side.

If the triangle is not a right triangle but you know two sides and the included angle, use the Law of Cosines: \(c^2 = a^2 + b^2 - 2ab \cos(C)\), where \(C\) is the angle opposite side \(c\). Substitute the known values and solve for the missing side.

If you know two angles and one side, use the Law of Sines: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\). Use this to find the missing side by setting up a proportion with the known side and angle.

After setting up the appropriate equation, simplify and solve algebraically for the missing side length. Since no calculator is allowed, use exact values of sine or cosine for common angles (like 30°, 45°, 60°) or simplify the square roots as needed.

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.

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 a missing side length when two sides are known.

Right Triangle Properties

Understanding that the triangle is right-angled allows the use of specific relationships like the Pythagorean theorem and trigonometric ratios. Recognizing the right angle is crucial for applying these methods correctly.

Exact Values and Simplification

Since the problem specifies not to use a calculator, it is important to work with exact values and simplify square roots or expressions manually. This skill helps in expressing the answer in simplest radical form.

Find the length of the remaining side of each triangle. Do not use a calculator.<IMAGE>