Explanation Given information: The triangle: Formula used: Law of cosine: a 2 = b 2 + c 2 − 2 b c cos A , where a , b , c are sides of a triangle, and the angles opposite to the sides a , b , c are A , B , C respectively. Area of triangle = 1 2 × base × height Calculation: Here, from the triangle, b = 5 , c = 9 , and A = 40 ∘ . By using law of cosine, ⇒ a 2 = 5 2 + 9 2 − 2 ( 5 ) ( 9 ) cos 40 ∘ ⇒ a 2 = 106 − 90 ⋅ ( 0.7660444431 ) ⇒ a 2 = 106 − 68.94399988 ⇒ a 2 = 37.05600012 ⇒ a = ± 6.087363971 ≈ ± 6.09 As the length of the side is never negative, so a ≈ 6.09 . Now, to find angle B , By using law of cosine, ⇒ b 2 = a 2 + c 2 − 2 a c cos B ∘ ⇒ 5 2 = ( 6.09 ) 2 + 9 2 − 2 ( 6.09 ) ( 9 ) cos B ∘ ⇒ 25 − 81 − 37.0881 = − 2 ( 6.09 ) ( 9 ) cos B ∘ ⇒ − 93.0881 = − 109.62 cos B ∘ ⇒ cos B ∘ = 93.0881 109.62 ⇒ cos B ∘ = 93

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ISBN: 9780134775173

Author: FRESH

Publisher: VST

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Chapter 12, Problem 12CR

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To calculate: The dimensions of a triangle and find its area where the triangle is

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Chapter 12, Problem 11CR

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Chapter 12 Solutions

EBK PRECALCULUS

Ch. 12.1 - Prob. 1AYU Ch. 12.1 - Prob. 2AYU Ch. 12.1 - Prob. 3AYU Ch. 12.1 - Prob. 4AYU Ch. 12.1 - Prob. 5AYU Ch. 12.1 - Prob. 6AYU Ch. 12.1 - Prob. 7AYU Ch. 12.1 - Prob. 8AYU Ch. 12.1 - Prob. 9AYU Ch. 12.1 - Prob. 10AYU

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The dimensions of a triangle and find its area where the triangle is

Solution Summary: The author calculates the dimensions of a triangle and its area by using the law of cosine.

To calculate: The dimensions of a triangle and find its area where the triangle is

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Chapter 12 Solutions