교과서 질문
Give the exact value of each expression. See Example 5. tan 30°
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Ch. 2 - Acute Angles and Right Triangles
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
3장, 문제 52
Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Height of a Tower The angle of depression from a television tower to a point on the ground 36.0 m from the bottom of the tower is 29.5°. Find the height of the tower.
검증된 단계별 안내1
Draw a right triangle representing the situation: the tower is the vertical side (height h), the distance from the tower to the point on the ground is the horizontal side (36.0 m), and the line of sight from the top of the tower to the point on the ground forms the hypotenuse.
Identify the angle of depression (29.5°) as the angle between the horizontal line from the top of the tower and the line of sight down to the point on the ground. This angle is congruent to the angle between the ground and the line of sight inside the triangle.
Use the tangent function, which relates the opposite side (height of the tower h) to the adjacent side (distance 36.0 m) in a right triangle: \(\tan(29.5^\circ) = \frac{h}{36.0}\).
Rearrange the equation to solve for the height h: \(h = 36.0 \times \tan(29.5^\circ)\).
Calculate the value of \(\tan(29.5^\circ)\) using a calculator and multiply by 36.0 to find the height of the tower.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Angle of Depression
The angle of depression is the angle formed between the horizontal line from the observer's eye and the line of sight to an object below the horizontal. In this problem, it helps relate the observer's viewpoint at the top of the tower to the point on the ground, allowing the use of trigonometric ratios.
추천 영상:
04:46
Coterminal Angles
Right Triangle Trigonometry
The problem involves a right triangle formed by the tower height, the horizontal distance from the tower base, and the line of sight. Using trigonometric functions like tangent, which relates opposite and adjacent sides, allows calculation of the unknown height.
추천 영상:
04:3945-45-90 Triangles
Tangent Function
The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the adjacent side. Here, tan(29.5°) = height / 36.0 m, which can be rearranged to find the tower's height by multiplying the tangent of the angle by the horizontal distance.
추천 영상:
5:43Introduction to Tangent Graph
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교과서 질문
Solve each problem.See Examples 3 and 4. Distance from the Ground to the Top of a Building The angle of depression from the top of a building to a point on the ground is 32°30'. How far is the point on the ground from the top of the building if the building is 252 m high?
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교과서 질문
Solve each problem. See Examples 1–4. Altitude of a Triangle Find the altitude of an isosceles triangle having base 184.2 cm if the angle opposite the base is 68°44'.
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