Prove the Law of Cosines, c 2 = a 2 + b 2 2ab cos ,

Question:

Prove the Law of Cosines, c₂= a₂+ b₂− 2ab cos θ, by referring to Figure 28. Hint: Consider the right triangle ΔPQR.

S 0 a a sin 0 b R 1 P C b-a cos 0 Q

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 31, 2023 04:28 AM

See More Questions

The four-sided gure shown in Figure P26 consists of two triangles having a common side a. The law of cosines for the top triangle states that a 2 = b 2 1 + c 2 1 - 2b 1 c 1 cos A 1 and a similar...
1. The standard form of the Law of Cosines for cos B = a2 + c2 b2 / 2ac is ________. 2. When solving an oblique triangle given three sides, use the ________ form of the Law of Cosines to solve for...
Illustrate local linearity for (x) = x 2 by zooming in on the graph at x = 0.5 (see Example 6). Hypotenuse 5 FIGURE 16 FIGURE 17 a Adjacent 2 (o Opposite 21 EXAMPLE 6 For between 0 and 27, the...
Selected accounts from the ledger of Restoration Arts for the fiscal year ended April 30, 2019, are as follows: Prepare a statement of owner's equity for the year. Apr 30 Doug Stone Capital Doug...
A boy whirls a ball on a string in a horizontal circle of radius 0.8 m. How many revolutions per minute must the ball make if the magnitude of its centripetal acceleration is to be the same as the...
What are creative bookkeeping techniques? Provide three examples.
Briefly describe design classes: utility, control, and boundary. How do they differ from entity classes?
Tel-Com Company, a telephone service and supply company, has just completed its fourth year of operations. The direct write-off method of recording bad debt expense has been used during the entire...
Discuss three social and legal concerns for the internet and e-business. Be specific and provide examples
Verify that (v) w = (v w) for any scalar .
Verify the Distributive Law: M. n + A. n = (M + A) .n
Indicate whether each of the following statements is true or false by writing T or F in the answer c olumn. A direct, unqualifi ed rejection terminates an offer.
Solve the following Cauchy-Euler differential equations: (a) 4ry' + 4ry - y = 0. (b) ry" + 10xy' + 8y = 0. (c) ry" - 6y = 0. (2) Solve the Cauchy-Euler DE by variation of parameters method: (a) xy" -...
Suppose that you have a piece of land to sell and you have two buyers. If the first buyer receives a fraction of the piece of land, the buyer will pay you U(x) dollars. Similarly, the second buyer...
a) 1 January, collected $10,000 cash from accounts receivable b) January, prepaid rent $24,000 for the next 4 months. c) 1 January, paid $8,000 of accounts payable, which related to inventory...
Using this data: Determine the sample size at 95% of confidence level and 3% of accuracy N=Z2 (1-P)p S
56 7 8 9 1 Calculate the following: the predetermined manufacturing overhead application rate, the budgeted direct labour hourly rate, the actual direct labour hours worked during the year and the...
Why does allocating costs using an ABC system not change the total reported income for the organization as a whole?
Differentiate. y = ln(3x + 1) ln(5x + 1)
Establish identity. cos 0 + sin 0 sin 0 sin 0 cot 0 + cos? 0
Establish identity. (2 cos? e 1)? cos e sin* 0 = 1 2 sin? e
Establish identity. 1 - 2 cos? 0 sin 0 cos 0 = tan 0 cot 0
1. Let X be the subspace of R3 spanned by the vectors (1,-1,0) and (1,1,1). The subspace X is a plane in R; find a Cartesian equation of this plane. Hence, or otherwise, find a basis of X+..
The University of Malaya Engineering Students Society is planning a six day trip to the national conference in Penang. For transportation, the group will rent a car from either the Motor Pool or a...
RENTAL PRICE 8. Links between factor markets Consider the markets for factors of production, such as labor and capital, to produce furniture in the United States before the invention of electric...

Prove the Law of Cosines, c 2 = a 2 + b 2 2ab cos ,

Question:

S 0 a a sin 0 b R 1 P C b-a cos 0 Q

Step by Step Answer:

We denote the vertices of the triangle by S Q and R Since RO RS SO we have ...View the full answer

Calculus

Students also viewed these Mathematics questions