Prove the Law of Cosines If a triangle has sides with lengths a, b, and c, and is the angle between the sides with lengths a and b, then c 2 a 2 b 2 2ab cos Introduce a coordinate system so that is in standard position, as in the figure Express x and y in terms of and then use the distance formula ...

From the figure in the text we see that x b cos ...

Prove the Law of Cosines: If a triangle has sides with lengths a, b, and c, and

Question:

Prove the Law of Cosines: If a triangle has sides with lengths a, b, and c, and θ is the angle between the sides with lengths a and b, then

c² = a² + b² - 2ab cos θ

Introduce a coordinate system so that θ is in standard position, as in the figure. Express x and y in terms of θ and then use the distance formula to compute c.]

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

Step by Step Answer:

Related Book For answer-question

Calculus Early Transcendentals

ISBN: 978-1285741550

8th edition

Authors: James Stewart

See More Books

Question Posted: Oct 11, 2022 05:23 AM

See More Questions

Use the figure to prove the law of cosines (which is a generalization of the Pythagorean theorem): c 2 = a 2 + b 2 - 2ab cos . (b cos 0, b sin 0) b' a (a, 0)
The Law of Cosines was used to solve a triangle in the two-solution case of SSA. Can the Law of Cosines be used to solve the no-solution and single-solution cases of SSA? Explain.
The law of cosines for a triangle states that a 2 = b 2 + c 2 - 2bc cosA, where a is the length of the side opposite the angle A, and b and c are the lengths of the other sides. a. Use MuPAD to solve...
Why do countries respond differently in terms of flexibility and worklife balance to what seem similar economic pressures?
Consider the normal curves shown at the right. Which normal curve has the greatest mean? Which normal curve has the greatest standard deviation? a. Find the location of the line of symmetry of each...
Find h' in terms of f' and g'. h(x) = f(g(sin 4x))
The IRR of this investment is located at which point? a. A b. C c. D d. E
McKnight Handcraft is a manufacturer of picture frames for large retailers. Every picture frame passes through two departments: the assembly department and the finishing department. This problem...
Give any statement as an example to explain data manipulation language nature of SQL.?
Following is the chart of accounts of the C. Lucern Clinic: Assets 111 Cash 113 Accounts Receivable 115 Supplies 117 Prepaid Insurance 124 Equipment Liabilities 221 Accounts Payable Owners Equity 311...
In order to find the distance |AB|across a small inlet, a point C was located as in the figure and the following measurements were recorded: C = 103 o |AC| = 820 m |BC| = 910 m Use the Law of Cosines...
Find all values of x in the interval [0, 2] that satisfy the inequality. sin x > cos x
Burtard Company develops and sells graphics software for use by architects. Journalize the entries to record the following selected transactions of Burtard Company: a. Purchased for cash $450,000 of...
Question 4 Cash Flow Statements (40 marks). PART A- This page - direct approach (30 marks) PART B- Next page - indirect approach (10 marks) The financial statements of Suns Limited are presented...
A logistics center in Mexico City is for sale. The price is 40million pesos. The NOI in the next year is projected to be 2million pesos. Industrial development is just as hot as it is here,and the...
You have been recently promoted to a managerial position in your company. You are tasked with leading a team of employees to increase the company's productivity and profitability. Your team comprises...
Q2) (A)Represent this graph into matrix and list B A C (C) Using the graph, classify each sequence as a walk, a path or a circuit A E F (3) C) d) e D B Walk D E Path a) FDCA BE b) AC-D-E-BA c) ECD E...
A large potters wheel, having a moment of inertia of 18.7 kg-m^2 is spinning freely at 41.06 rpm. The potter drops a small but dense lump of clay onto the wheel, where it sticks a distance 0.362 m...
A hotel has designed a new system for room service delivery of breakfast that allows the customer to select a specific delivery time. The difference between the actual and requested delivery times...
Research an article from an online source, such as The Economist, Wall Street Journal, Journal of Economic Perspectives, American Journal of Agricultural Economics, or another academic journal. The...
If r(t) = t - 1 i + ln(2t2)j and h(t) = e-3t, find Dt[h(t)r(t)].
If r(t) = sin 2t i + cosh t j and h(t) = ln (3t - 2), find Dt[h(t)r(t)].
In Problem a-b, find the velocity v, acceleration a, and speed s at the indicated time t = t1. a. r(t) = 4ti + 5(t2 - 1)j + 2tk; t1 = 1 b. r(t) = ti + (t - 1)2j + (t - 3)3k; t1 = 0
Expand the following functions in power series about 1 (a) (b) z+1 z 23-1 (c) ex
The diagram shows equipment attached to a battery. Current DC power source Magnetic field lines N I In which direction will the wire XY move? Metal dish Conducting liquid
Find the power series expansion (or the first 5 terms of the power series) of at z=0 and its radius of convergence. e 1+2 centered

Prove the Law of Cosines: If a triangle has sides with lengths a, b, and c, and

Question:

Step by Step Answer:

From the figure in the text we see that x b cos ...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions