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Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 12th EditionCh. 2 - Acute Angles and Right Triangles문제 53
3장, 문제 53

Solve each problem. See Examples 3 and 4. Length of a Shadow Suppose that the angle of elevation of the sun is 23.4°. Find the length of the shadow cast by a person who is 5.75 ft tall.
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검증된 단계별 안내
1
Identify the right triangle formed by the person, the shadow, and the line of sight to the sun. The person's height is the side opposite the angle of elevation, and the shadow length is the adjacent side.
Label the angle of elevation as \(\theta = 23.4^\circ\), the height of the person as the opposite side \(O = 5.75\) ft, and the shadow length as the adjacent side \(A\) (which we need to find).
Use the tangent trigonometric ratio, which relates the opposite side and adjacent side in a right triangle: \(\tan(\theta) = \frac{O}{A}\).
Rearrange the formula to solve for the shadow length \(A\): \(A = \frac{O}{\tan(\theta)}\).
Substitute the known values into the equation: \(A = \frac{5.75}{\tan(23.4^\circ)}\), and then calculate the value of \(A\) to find the length of the shadow.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

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

Angle of Elevation

The angle of elevation is the angle formed between the horizontal ground and the line of sight to an object above the horizontal. In this problem, it represents the sun's position relative to the person, which helps determine the shadow length using trigonometric ratios.
추천 영상:
04:46
Coterminal Angles

Right Triangle Trigonometry

The situation forms a right triangle where the person's height is one leg, the shadow length is the other leg, and the angle of elevation is between the shadow and the line to the sun. Using trigonometric functions like tangent relates these sides and the angle.
추천 영상:
04:39
45-45-90 Triangles

Tangent Function

Tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, tan(23.4°) = height of person / length of shadow, allowing calculation of the shadow length by rearranging the formula.
추천 영상:
5:43
Introduction to Tangent Graph
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