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If the hypotenuse of a right triangle has length 9 feet and one of the other sides has length 2 feet, what is the length of the remaining side, in feet?


\sf A) √(11)

\sf B) √(7)

\sf C) √(85)

\sf D) √(77)

\sf E) 7

User Eliane
by
6.6k points

2 Answers

1 vote
  • Hypotenuse=H=9ft
  • Base=B=2ft

Apply Pythagorean theorem

  • P²=H²-B²
  • P²=9²-2²
  • P²=81-4
  • P²=77
  • P=√77

Option D

User Harmelodic
by
7.2k points
9 votes

Answer:


\sf D) √(77) \: ft

Explanation:

Given that,

→ Perpendicular (x) = ?

→ Hypotenuse (h) = 9 feet

→ Base (b) = 2 feet

Now by using the Phythagoras theorem,

→ (Hypotenuse)² = (Perpendicular)² + (Base)²

→ (h)² = (x)² + (b)²

→ (9)² = (x)² + (2)²

→ 81 = (x)² + 4

→ (x)² = 81 - 4

→ (x)² = 77

→ [ x = √(77) ]

Thus, length of remaining side is √(77) ft.

User Synthetic
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6.4k points