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m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft. This can be obtained using the Laws of cosine formula and Laws of sine formula.
<h3>Find the required angles and sides:</h3>- Laws of cosine formula,
In a triangle ABC,
⇒ a² = b² + c² - 2bc cos A
⇒ b² = a² + c² - 2ac cos B
⇒ c² = a² + b² - 2ab cos C
where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.
- Laws of sine formula,
In a triangle ABC,
⇒
where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.
In the question we can use the laws of cosine formula and laws of sine formula,
5) Given that,
AB = c = 13 km
AC = b = 21 km
m∠A = 91°
By using Laws of cosine formula,
⇒ a² = b² + c² - 2bc cos A
a² = 21² + 13² - 2(21)(13) cos 91°
a² = 441 + 169 - 546 (-0.0174524064)
a² = 610 + 9.52901391 = 619.529014
⇒ a = 24.89 km
By using Laws of sine formula,
⇒
sin 91°/24.89 = sin B/21
sin B = 0.999847695×21/24.89 = 0.843583833
⇒ m∠B = 57.52°
6) Given that,
AB = c = 11 cm
BC = a = 13 cm
AC = b = 14 cm
By using Laws of cosine formula,
⇒ b² = a² + c² - 2ac cos B
14² = 13² + 11² - 2(13)(11) cos B
196 = 169 + 121 - 286 cos B
196 = 290 - 286 cos B
cos B = 94/286
cos B = 0.328671329
⇒ m∠B = 70.8°
7) Given that,
AC = b = 24 km
BC = a = 26 km
m∠C = 134°
By using Laws of cosine formula,
⇒ c² = a² + b² - 2ab cos C
c² = 26² + 24² - 2(26)(24) cos 134°
c² = 676 + 576 - 1248 (-0.69465837)
c² = 1252 + 866.933646 = 2118.93365
⇒ AB = c = 46.03 km
8) Given that,
AB = c = 26 ft
BC = a = 21 ft
m∠B = 112°
By using Laws of cosine formula,
⇒ b² = a² + c² - 2ac cos B
b² = 21² + 26² - 2(21)(26) cos 112°
b² = 441 + 676 - 1096 (-0.374606593)
b² = 1117 + 410.568826 = 1527.56883
⇒ AC = b = 39.08 ft
Hence m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft.
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Answer:
Step-by-step explanation:
Since the company wants to survey 500 customers by the countries visited, the number of samples from each country will be proportional to the number of customers.
For UK, Number of Samples
For France, Number of Samples
For Spain, Number of Samples
For Italy, Number of Samples
The completed table therefore is: