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vladimir2022 [97]
3 years ago
5

In triangle XYZ, mZZ > mZX + mZY. Which must be true about AXYZ?

Mathematics
1 answer:
Semmy [17]3 years ago
4 0

Answer:

  • D. m∠X + m∠Y < 90°

Step-by-step explanation:

<h3>Given</h3>
  • ΔXYZ with m∠Z > m∠X + m∠Y
<h3>Options</h3>

<u>m∠X + m∠Z < 90°</u>

  • incorrect, the sum of these two angles should be > 90°

<u>m∠Y > 90°</u>

  • incorrect, it should be < 90°

<u>∠X and ∠Y are complementary</u>

  • incorrect as angle Z is greater that the sum of angles X and Y, then sum of three angles would be greater than 180°

<u>m∠X + m∠Y < 90°</u>

  • correct, this is the only possible option
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3 years ago
Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance fr
AfilCa [17]

The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

  • Distance is defined to be the magnitude or size of displacement between two positions.
  • Note that the distance between two positions is not the same as the distance traveled between them.
  • Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

∴ l₁ = h₁/(sin(x°))

Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

Learn more about distance

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2 years ago
What is the sign of a^72*(-3/7) when a is a negative number
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What is the value of X?
Leviafan [203]

Answer:

w = 31

Step-by-step explanation:

To find the value of w:

 We know that the three angles in a triangle add to 180 degrees

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6w-6 = 180

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Divide each side by 6

6w/6 = 186/6

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3 years ago
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