Question

What is the length of side EF in the triangle? Please give a step by step explanation, I'm having lots of trouble finding the solution. Thank you!

Answer 1

`{\underline{\underline{\bf{Given:}}}}`

• A right-angled triangle DEF
• Measure of angle F = 90°
• Measure of side DF = 13.6 m
• Measure of side DE = 16.2 m

`{\underline{\underline{\bf{Need\:to\:find:}}}}`

• The measure of side EF.

`{\underline{\underline{\bf{Formula\:to\:be\:used:}}}}`

Pythagorean Theorem:

`\underline{\boxed{\sf{{Base}^(2)+{Perpendicular}^(2)={Hypotenuse}^(2)}}}`

`{\underline{\underline{\bf{Solution:}}}}`

According to the given data, we know the measures of Perpendicular and Hypotenuse. Hence, the measure of the base (Side FE) can be found by substituting the given measures in Pythagorean Theorem.

`\implies{\sf{{Base}^(2)+{Perpendicular}^(2)={Hypotenuse}^(2)}}`

`\implies{\sf{{EF}^(2)+{DF}^(2)={DE}^(2)}}`

`\implies{\sf{{EF}^(2)+{(13.6)}^(2)={(16.2)}^(2)}}`

`\implies{\sf{ EF = \sqrt{ {(16.2)}^(2) - {(13.6)}^(2) } }}`

`\implies{\sf{ EF = √( 262.44 - 184.96 ) }}`

`\implies{\sf{ EF = √(77.48 ) }}`

`\implies{\sf{EF=\red{\underline{\underline{8.802\:m}}}}}`

`{\underline{\underline{\bf{Required\:answer:}}}}`

• The length of side EF is 8.802 m.

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