Answer:
[tex] \huge{ \boxed{ \tt{17 \: cm}}}[/tex]
Option D is the correct choice.
☪ First , Let's know about right triangle , legs and hypotenuse :
- A right triangle is a triangle with an angle of 90°.
- The two sides that form the right angle are called legs.
- The opposite side of right angle is the hypotenuse.
☥ Let's explore about The Pythagorean Theorem :
- Pythagoras was one of the first mathematician to recognize the relationship between the sides of a right triangle. This special relationship forms ' The Pythagorean Theorem '.
- The Pythagorean theorem states that the sum of the squares of the legs of a right triangle equals the square of the length of a hypotenuse.
- In algebraic terms , The Pythagorean Theorem is stated as : [tex] \boxed{ \sf{ {a}^{2} + {b}^{2} = {c}^{2} }}[/tex]
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☯ Now , let's start to solve :
✑ [tex] \underline{ \underline{ \text{Given}}} : [/tex]
✑ [tex] \underline{ \underline{ \text{To\: Find}}} : [/tex]
- Length of a hypotenuse ( c )
✐ [tex] \underline{ \bold{ \underline{Using \: Pythagorean \: Theorem}}} \: : [/tex]
☞ [tex] \boxed{ \bold{ \sf{ {a}^{2} + {b}^{2} = {c}^{2} }}}[/tex]
Substitute the known values :
↦ [tex] \sf{ {8}^{2} + {15}^{2} = {c}^{2}}[/tex]
↦ [tex] \sf{64 + 225 = {c}^{2} }[/tex]
↦ [tex] \sf{289 = {c}^{2} }[/tex]
↦ [tex] \sf{ {c}^{2} = 289 }[/tex]
Take the square roots of both sides :
↦ [tex] \sf{ \sqrt{ {c}^{2} } = \sqrt{289}} [/tex]
↦ [tex] \boxed{ \sf{c = 17 \: cm}}[/tex]
The length of the hypotenuse is [tex] \boxed{ \bold{ \text{17 \: cm}}}[/tex].
And we're done!!
Hope I helped!
Have a wonderful day ! ツ
~TheAnimeGirl ♡
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