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olga nikolaevna [1]
2 years ago
10

Find b such that the points A(2,b),B(5,5)and C(-6,0) are the vertices of right angled  with angle < BAC = 90 degree.​

Mathematics
2 answers:
kipiarov [429]2 years ago
7 0

The <BAC angle isn't a perfect right angle because the image was a photo

<em><u>If this helped, please consider picking this answer as the Brainliest Answer. Thank you!</u></em>

Inessa05 [86]2 years ago
7 0

Answer:

  • b = -3 or b = 8

Step-by-step explanation:

We know that the perpendicular lines have negative-reciprocal slopes.

In other words, their product is - 1.

<u>Find the slopes of AB and AC:</u>

  • m(AB) = (5 - b)/(5 - 2) = (5 - b) / 3
  • m(AC) = (0 - b)/(- 6 - 2) = - b / - 8 = b/8

<u>Find the the product of slopes and solve for b:</u>

  • (5 - b)/3 * b/8 = - 1
  • b(b - 5)/24 = 1
  • b(b - 5) = 24
  • b² - 5b - 24 = 0
  • b² - 8b + 3b - 24 = 0
  • b(b - 8) + 3(b - 8) = 0
  • (b + 3)(b - 8) = 0
  • b = - 3 or b = 8

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6 0
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Given that WA = 5x – 8 and WC = 3x + 2, find WB. A. WB = 5 B. WB = 8 C. WB = 10 D. WB = 17
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The rest of the question is the attached figure.
============================================
Δ AYW a right triangle at Y ⇒⇒⇒ ∴ WA² = AY² + YW²
And AY = YB ⇒⇒⇒ ∴ WA² = YB² + YW²   → (1)
Δ BYW a right triangle at Y ⇒⇒⇒ ∴ WB² = BY² + YW²  → (2)
From (1) , (2)  ⇒⇒⇒ ∴ WA = WB  →→ (3)
Δ CXW a right triangle at Y ⇒⇒⇒ ∴ WC² = CX² + XW²
And CX = XB ⇒⇒⇒ ∴ WC² = XB² + XW²   → (4)
Δ BXW a right triangle at Y ⇒⇒⇒ ∴ WB² = XB² + XW²  → (5)
From (4) , (5)  ⇒⇒⇒ ∴ WC = WB  →→ (6)
From (3) , (6)
WA = WB = WC
given ⇒⇒⇒ WA = 5x – 8 and WC = 3x + 2
∴ <span> 5x – 8 = 3x + 2</span>
Solve for x ⇒⇒⇒ ∴ x = 5
∴ WB = WA = WC = 3*5 + 2 = 17

The correct answer is option D. WB = 17






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