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Chapter 9: Q. 1 (page 611)

In a triangle with sides a, b, c and angles A, B, C, the Law of Cosines states that ____.

Short Answer

Expert verified

In a triangle with sides a, b, c and angles A, B, C, the Law of Cosines states that,

$a^{2} = b^{2} + c^{2} - 2 b c \times \cos A b^{2} = a^{2} + c^{2} - 2 a c \times \cos B c^{2} = a^{2} + b^{2} - 2 a b \cos C$ .

Step by step solution

01

Step 1. Given Information

We are given a triangle with sides a, b, c and angles A, B, C.

We have to fill in the blanks.

02

Step 2. Completing the statement

The law of cosine will be,

$a^{2} = b^{2} + c^{2} - 2 b c \times \cos A b^{2} = a^{2} + c^{2} - 2 a c \times \cos B c^{2} = a^{2} + b^{2} - 2 a b \cos C$

Hence the given statement can be completed as,

In a triangle with sides a, b, c and angles A, B, C, the Law of Cosines states that,

$a^{2} = b^{2} + c^{2} - 2 b c \times \cos A b^{2} = a^{2} + c^{2} - 2 a c \times \cos B c^{2} = a^{2} + b^{2} - 2 a b \cos C$

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Most popular questions from this chapter

In Problems 39–54, the polar coordinates of a point are given. Find the rectangular coordinates of each point.

$(8.1, 5.2)$

$\cos \frac{2 π}{3} =________.$

In Problems 39–54, the polar coordinates of a point are given. Find the rectangular coordinates of each point.

$(- 3.1, 182 °)$

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(- 3, π)$

In Problems 13–28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

$r \sin θ = 4$

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