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Ch. 7 - Applications of Trigonometry and Vectors
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 12th EditionCh. 7 - Applications of Trigonometry and Vectors문제 1
8장, 문제 1

Use the law of sines to find the indicated part of each triangle ABC.


Find b if C = 74.2°, c = 96.3 m, B = 39.5

검증된 단계별 안내
1
Identify the known parts of the triangle: angle C = 74.2°, side c = 96.3 m (opposite angle C), and angle B = 39.5°. We need to find side b, which is opposite angle B.
Recall the Law of Sines formula: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\). We will use the relationship between sides b and c and their opposite angles B and C.
Set up the proportion using the Law of Sines: \(\frac{b}{\sin B} = \frac{c}{\sin C}\). Substitute the known values: \(\frac{b}{\sin 39.5^\circ} = \frac{96.3}{\sin 74.2^\circ}\).
Solve for side b by multiplying both sides by \(\sin 39.5^\circ\): \(b = \frac{96.3 \times \sin 39.5^\circ}{\sin 74.2^\circ}\).
Calculate the sine values for angles 39.5° and 74.2°, then perform the multiplication and division to find the length of side b.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

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

Law of Sines

The Law of Sines relates the sides and angles of a triangle by stating that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides. It is expressed as (a/sin A) = (b/sin B) = (c/sin C), and is useful for solving triangles when given two angles and one side or two sides and a non-included angle.
추천 영상:
가이드 코스
4:27
Intro to Law of Sines

Triangle Angle Sum Property

The sum of the interior angles in any triangle is always 180°. This property allows you to find the missing angle when two angles are known, which is essential before applying the Law of Sines if not all angles are given.
추천 영상:
가이드 코스
4:47
Sum and Difference of Tangent

Solving for Unknown Sides

Once the Law of Sines is set up, you can solve for an unknown side by rearranging the formula to isolate the side length. This involves substituting known angle measures and side lengths, then calculating the unknown side using algebraic manipulation and trigonometric values.
추천 영상:
가이드 코스
4:18
Finding Missing Side Lengths
관련 실천
교과서 질문

Fill in the blank(s) to correctly complete each sentence.


A triangle that is not a right triangle is a(n) _________ triangle.

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교과서 질문

Which one of the following sets of data does not determine a unique triangle?

a. A = 50°, b = 21, a = 19

b. A = 45°, b = 10, a = 12

c. A = 130°, b = 4, a = 7

d. A = 30°, b = 8, a = 4

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교과서 질문

Use the law of sines to find the indicated part of each triangle ABC.


Find B if C = 51.3°, c = 68.3 m, b = 58.2 m

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교과서 질문

In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?

a. two triangles

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교과서 질문

In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?

b. exactly one triangle

<IMAGE>

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교과서 질문

CONCEPT PREVIEW Assume a triangle ABC has standard labeling.


a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.


b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.


a, b, and C

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