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jeyben [28]
2 years ago
7

A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 f

eet from the base of the pole.
A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h.

What is the height of the pole? Round to the nearest hundredth.
12.00 feet
19.60 feet
24.17 feet
38.40 feet

Mathematics
1 answer:
krok68 [10]2 years ago
4 0

✰ <u>Concept</u><u> </u><u>Used</u><u> </u><u>:</u><u>-</u>

⠀

In this question, we can clearly observer that the diagram shows a right angled triangle. And, we have been provided with the value of base, and the value of hypotenuse, using the pythagoras theorem, now we can easily find out the value of the perpendicular i.e. the value of the side h. According to the pythagoras theorem, square of hypotenuse is equal to the sum of square of perpendicular and square of side respectively. Therefore, square of side is equal to the difference of square of hypotenuse and square of perpendicular.

⠀

✰ <u>Given</u><u> </u><u>Information</u><u> </u>:-

⠀

  • Hypotenuse = 22 ft.
  • Base = 10 ft.

⠀

✰ <u>To Find</u><u> </u><u>:</u><u>-</u>

⠀

  • The value of side or the perpendicular

⠀

✰ <u>Formula</u><u> </u><u>Used</u><u> </u><u>:</u><u>-</u>

⠀

\star \:  \underline{ \boxed{ \purple { \sf  {Side}^{2}  =  {Hypotenuse}^{2}  -  {Base}^{2}  }}} \:  \star

⠀

✰ <u>Solution</u><u> </u><u>:</u><u>-</u>

⠀

\sf \longrightarrow  {Side}^{2} =   {(22 \: ft)}^{2}  -  {(10 \: ft)}^{2}  \:  \:  \:  \\  \\  \\ \sf \longrightarrow  {Side}^{2} =   {484 \: ft}^{2}  -  {100 \: ft}^{2}  \:  \:  \: \:  \:  \:   \\  \\  \\ \sf \longrightarrow  {Side}^{2} =   {384 \: ft}^{2}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\  \\ \sf \longrightarrow  {Side}^{} =   \sqrt{ {384 \: ft}^{2} }  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\  \\ \sf \longrightarrow  {Side}^{} =   \underline{ \boxed{ \frak{ \green{19.60 \: ft}}}} \:  \star \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\

Thus, option B. 19.60 ft. is the correct option.

⠀

\underline{\rule{230pt}{2pt}} \\  \\

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