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°

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)