List the angles of ∆ abc from smallest to largest. Ab = 20, bc = 12, ca = 10.

Answers

Answer 1

The angle of the triangle ABC from smallest to largest are approximately 22°, 27° and 131°.

The sides of the triangle are as follows;

AB = 20

BC = 12

AC = 10

Let's find ∠A using cosine rule,

a² = b² + c² - 2bc cos A

cos A = b² + c² - a² / 2bc

Therefore,

cos A = 10² + 20² - 12²  / 2 × 10 × 20

cos A = 100 + 400 - 144 / 400

cos A = 356 / 400

cos A = 0.89

A = cos⁻¹ 0.89

A = 27.1267531173

∠A ≈ 27°

Using sine rule let's find ∠B

12 / sin 27 = 10 / sin B

cross multiply

12 sin B = 10 sin 27

sin B = 10 sin 27 / 12

sin B = 10 × 0.45399049974  / 12

sin B = 4.5399049974  / 12

B = sin⁻¹ 0.37832541645

B = 22.2299936087

∠B = 22°

Using sum of triangle theorem let's find ∠C

∠C = 180 - 27 - 22

∠C = 131°

The angles from smallest to largest are approximately 22°, 27° and 131°.

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It is very important to help people when they are in need. The person who helped Prospero and Miranda was Gonzalo.

Gonzalo   is known to be a very old and honest lord in the passage. He helped Prospero and Miranda to escape only when Antonio has usurped Prospero's title.

In The Tempest, Gonzalo greatly helped Prospero and Miranda. This is because they were banished from Italy. He was known to have given them with food, water, magic books, etc. so that they can survive at sea.

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The conclusion which can be drawn with respect to the nature of an exchange-rate table in December 2013 is that: B. It would look different because exchange rate tables change constantly.

An exchange rate can be defined as a number that is used to denote or represent the financial value of a currency in comparison with another currency.

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Answer: B - It would look different because exchange rate tables change constantly.

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Answers

No product results in -1, hence δlmn is NOT a right triangle showing that  lydia's assertion is incorrect

Perpendicular lines

In order to determine whether triangle lmn  is right-angled, we need to determine the slope of lm, ln, and mn first as shown:

For the slope of lm:

[tex]m_{lm} = \frac{2-0}{2-0}\\ m_{lm} =2/2\\m_{lm} =1[/tex]

For the slope of ln:

[tex]m_{ln} = \frac{-1-0}{2-0}\\m_{ln} =-1/2\\[/tex]

For the slope of mn:

[tex]m_{mn} = \frac{-1-2}{2-2}\\m_{ln} =-3/0 = \infty\\[/tex]

If any of the two lines is perpendicular, hence the triangle lmn is right-angled.

To check, we will take the product of the slopes and see if it is equivalent to -1.

Product of slope lm and ln

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Answer:

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Explanation:

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ProcedureGrammatical structure

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