Find the measure of angle eight in each triangle round each answer to the nearest 10th

# m∠A = 65.3°

# m∠A = 25.8°

# m∠A = 22.7°

Step-by-step explanation:

* Lets revise the trigonometry function to solve the problem

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Lets solve the problems

# In Δ ABC

∵ m∠B = 90°

∵ AB = 2.3 ⇒ adjacent to angle A

∵ BC = 5 ⇒ apposite to angle A

- To find m∠A use the tangent function because we have opposite

  and adjacent sides

∴ tan A = BC/AB

∴ tan A = 5/2.3 ⇒ use tan^-1 to find m∠A

∴ m∠A =

* m∠A = 65.3°

# In Δ ABD

∵ m∠B = 90°

∵ AB = 5.4 ⇒ adjacent to angle A

∵ DA = 6 ⇒ the hypotenuse

- To find m∠A use the cosine function because we have adjacent

  and hypotenuse sides

∴ cos A = AB/DA

∴ cos A = 5.4/6 ⇒ use cos^-1 to find m∠A

∴ m∠A =

* m∠A = 25.8°

# In Δ ABE

∵ m∠B = 90°

∵ EB = 2.4 ⇒ opposite to angle A

∵ EA = 6.8 ⇒ the hypotenuse

- To find m∠A use the sine function because we have opposite

  and hypotenuse sides

∴ sin A = EB/EA

∴ sin A = 2.4/6.8 ⇒ use sin^-1 to find m∠A

∴ m∠A =

* m∠A = 22.7°

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the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: