교과서 질문
Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 54°
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Ch. 1 - Trigonometric Functions
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
2장, 문제 15
Solve each problem. Length of a Road A camera is located on a satellite with its lens positioned at C in the figure. Length PC represents the distance from the lens to the film PQ, and BA represents a straight road on the ground. Use the measurements given in the figure to find the length of the road. (Data from Kastner, B., Space Mathematics, NASA.)
검증된 단계별 안내1
Identify the right triangles formed in the figure involving points P, C, Q, B, and A. Typically, the camera lens at C, the film at PQ, and the road segment BA form similar triangles due to the geometry of the setup.
Use the property of similar triangles: corresponding sides are proportional. Set up a proportion relating the length of the road segment BA to the length of the film segment PQ, using the distances PC and the corresponding distances on the ground.
Write the proportion as \(\frac{BA}{PQ} = \frac{PC}{\text{distance on ground corresponding to } PQ}\), where the 'distance on ground corresponding to PQ' is the segment on the ground that corresponds to PQ in the similar triangles.
Solve the proportion for the length of the road segment BA by cross-multiplying and isolating BA on one side of the equation.
Substitute the given numerical values from the figure into the equation and simplify to find the length of the road BA (do not calculate the final numeric value here, just set up the expression).
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.
Similar Triangles
Similar triangles have the same shape but different sizes, with corresponding angles equal and sides proportional. This concept allows us to set up ratios between corresponding sides to find unknown lengths, such as the length of the road, by comparing the satellite's camera setup to the ground measurements.
추천 영상:
5:35
30-60-90 Triangles
Proportionality in Triangles
Proportionality refers to the equality of ratios between corresponding sides of similar triangles. By establishing a proportion between the known distances (like PC and PQ) and the unknown length (BA), we can solve for the unknown length using cross-multiplication.
추천 영상:
5:3530-60-90 Triangles
Application of Trigonometric Ratios
Trigonometric ratios (sine, cosine, tangent) relate angles to side lengths in right triangles. Understanding these ratios helps interpret the geometric relationships in the figure, especially if angles or heights are involved, to calculate distances indirectly when direct measurement is not possible.
추천 영상:
6:04Introduction to Trigonometric Functions
관련 실천
교과서 질문
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
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교과서 질문
Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―8 , 15)
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교과서 질문
Find the measure of each marked angle.
696
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교과서 질문
Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 10°
745
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교과서 질문
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel.
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