Question

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

Answer 1

`\sf\large \green{\underbrace{\red{Answer⋆}}}:`

TE = 12 feet

Explanation:

`\textsf {\underline{ \large {To find :-}}}`

length of TE

`\sf {\underline {\large {Given :-}}}`

TS = 35 feet

SE = 37 feet

`\sf{ \green {\underline{ \underline {\huge{Solution :-}}}}}`

According to Pythagoras theorem

`\sf \pink {hypotenuse^(2) = {perpendicular}^(2) + {base}^(2) }`

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

`\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 √(144) = base \\ \\ \sf \implies { \fbox {\blue {12 = base}}}`

It's means our TE is 12 feet

Answer 2

Hey ! there

Answer:

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

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 :

`\quad \longmapsto \qquad \:SE {}^(2) = TS {}^(2) + TE {}^(2)`

Substituting values :

`\quad \longmapsto \qquad \:37 {}^(2) = 35 {}^(2) + TE {}^(2)`

Simplifying it ,

`\quad \longmapsto \qquad \:1369 = 1225 + TE {}^(2)`

Subtracting 1225 on both sides :

`\quad \longmapsto \qquad \:1369 - 1225 = \cancel{1225} + TE {}^(2) - \cancel{1225}`

We get ,

`\quad \longmapsto \qquad \:144 = TE {}^(2)`

Applying square root to both sides :

`\quad \longmapsto \qquad \ √( 144) = \sqrt{TE {}^(2)}`

We get ,

`\quad \longmapsto \qquad \: \red{\underline{\boxed{\frak{TE = 12 \: feet}}}} \quad \bigstar`

• 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 .

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