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O ADDITIONAL TOPICS IN TRIGONOMETRYTry again...MaxSolving a word problem using the law of sinesinEspañolAlonzo and Jane are standing on a riverbank, 110 meters apart, at points A and B respectively. (See the figure below.) Jane is 140 meters from a house locatedacross the river at point C. Suppose that angle A (angle BA C) is 40°. What is the measure of angle B (angle ABC)? Round your answer to the nearest tenth ofa degree.110 mAB40°O?X140 mАаС4 4ш

Question

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O ADDITIONAL TOPICS IN TRIGONOMETRY
Try again...
Max
Solving a word problem using the law of sines
in
Español
Alonzo and Jane are standing on a riverbank, 110 meters apart, at points A and B respectively. (See the figure below.) Jane is 140 meters from a house located
across the river at point C. Suppose that angle A (angle BA C) is 40°. What is the measure of angle B (angle ABC)? Round your answer to the nearest tenth of
a degree.
110 m
A
B
40°
O
?
X
140 m
Аа
С
4 4
ш
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O ADDITIONAL TOPICS IN TRIGONOMETRY Try again... Max Solving a word problem using the law of sines in Español Alonzo and Jane are standing on a riverbank, 110 meters apart, at points A and B respectively. (See the figure below.) Jane is 140 meters from a house located across the river at point C. Suppose that angle A (angle BA C) is 40°. What is the measure of angle B (angle ABC)? Round your answer to the nearest tenth of a degree. 110 m A B 40° O ? X 140 m Аа С 4 4 ш

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check_circleAnswer
Step 1

Given: A triangle ABC as in the figure below below. Suppose that

A 40°, b 110, and c = 140
110 m
B
40°
140 m
4 4
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A 40°, b 110, and c = 140 110 m B 40° 140 m 4 4

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Step 2

Formula used:

For any triangle given two sides and an included angle, the Law of Cosines and Law of Sines:

a2 bc2-2bc cos A
b2 ac-2ac cos B
c2 =b2+a-2ab cos C
( Law of Cosines
(Law of Cosines
( Law of Cosines)
sin A
sin B
sin C
(
Law of Sines)
b
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a2 bc2-2bc cos A b2 ac-2ac cos B c2 =b2+a-2ab cos C ( Law of Cosines (Law of Cosines ( Law of Cosines) sin A sin B sin C ( Law of Sines) b

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Step 3

By finding the value of ‘a&r...

a
b2c2-2bc cos A
a (110)(140)-2x110x140x cos 40°
a2 12100 19600-30800 x 0.766
a2 31700-23592.8
a28107.2
a =8107.2
a 90.03
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a b2c2-2bc cos A a (110)(140)-2x110x140x cos 40° a2 12100 19600-30800 x 0.766 a2 31700-23592.8 a28107.2 a =8107.2 a 90.03

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Trigonometry

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