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10 points, doing this one again because I got a wrong answer last time but regardless thank you for trying to help​

10 points doing this one again because I got a wrong answer last time but regardless thank you for trying to help class=

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TheAmethyst

Hey ! there

Answer:

  • Value of missing side i.e. TE is 12 feet

Step-by-step explanation:

In this question we are provided with a right angle triangle having TS - 35 ft and SE - 37 ft . And we are asked to find the missing side that is TE using Pythagorean Theorem .

Pythagorean Theorem : -

According to Pythagorean Theorem sum of squares of perpendicular and base is equal to square of hypotenuse in a right angle triangle i.e.

  • H² = P² + B²

Where ,

  • H refers to Hypotenuse

  • P refers to Perpendicular

  • B refers to Base

Solution : -

In the given triangle ,

  • Base = TE

  • Perpendicular = TS ( 35 feet )

  • Hypotenuse = SE ( 37 feet )

Now applying Pythagorean Theorem :

[tex] \quad \longmapsto \qquad \:SE {}^{2} = TS {}^{2} + TE {}^{2} [/tex]

Substituting values :

[tex] \quad \longmapsto \qquad \:37 {}^{2} = 35 {}^{2} + TE {}^{2} [/tex]

Simplifying it ,

[tex] \quad \longmapsto \qquad \:1369 = 1225 + TE {}^{2} [/tex]

Subtracting 1225 on both sides :

[tex] \quad \longmapsto \qquad \:1369 - 1225 = \cancel{1225} + TE {}^{2} - \cancel{1225}[/tex]

We get ,

[tex] \quad \longmapsto \qquad \:144 = TE {}^{2}[/tex]

Applying square root to both sides :

[tex] \quad \longmapsto \qquad \ \sqrt{ 144} = \sqrt{TE {}^{2}}[/tex]

We get ,

[tex] \quad \longmapsto \qquad \: \red{\underline{\boxed{\frak{TE = 12 \: feet}}}} \quad \bigstar[/tex]

  • Henceforth , value of missing side is 12 feet .

Verifying : -

Now we are verifying our answer using Pythagorean Theorem . We know that according to Pythagorean Theorem ,

  • SE² = TS² + TE²

Substituting value of SE , TS and TE :

  • 37² = 35² + 12²

  • 1369 = 1225 + 144

  • 1369 = 1369

  • L.H.S = R.H.S

  • Hence , Verified .

Therefore , our answer is correct .

#Keep Learning

[tex]\sf\large \green{\underbrace{\red{Answer⋆}}}:[/tex]

TE = 12 feet

Step-by-step explanation:

[tex] \textsf {\underline{ \large {To find :-}}}[/tex]

length of TE

[tex] \sf {\underline {\large {Given :-}}}[/tex]

TS = 35 feet

SE = 37 feet

[tex] \sf{ \green {\underline{ \underline {\huge{Solution :-}}}}}[/tex]

According to Pythagoras theorem

[tex] \sf \pink {hypotenuse^{2} = {perpendicular}^{2} + {base}^{2} }[/tex]

in the diagram

SE is our hypotenuse as it is front of 90°

TS is our perpendicular

TE is our base

So with the above formula we can find our base which is TE

[tex] \sf \implies {37}^{2} = {35}^{2} + {base}^{2} \\ \\ \sf \implies 1369 = 1225 + {base}^{2} \\ \\ \sf \implies 1369 - 1225 = {base}^{2} \\ \\ \sf \implies 144 = {base}^{2} \\ \\ \sf \implies \sqrt{144} = base \\ \\ \sf \implies { \fbox {\blue {12 = base}}}[/tex]

It's means our TE is 12 feet

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