Question

I can find the missing leg length
?
7
12.21

Answer 1

RIGHT TRIANGLE

Answer:

• 
  `\color{hotpink} \bold{10}`

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We can find the length of the missing side of the right triangle using the Pythagorean Theorem.

As you can see in the attached image, we are looking for b or the longer side/leg of the right triangle. (See the attached image for the right triangle.)

Using the formula c² = a² + b².

we let c=12.21 and a=7

• 
  `c {}^(2) = {a}^(2) + {b}^(2)`

• 
  `{12.21}^(2) = {7}^(2) + {b}^(2)`

• 
  `{149.0841} = {7}^(2) + {b}^(2)`

By transposition/adding the additive inverse of 49.

• 
  `{b}^(2) = {149.0841} - 49`

The difference of 149.0841 - 49 is 100.084

• 
  `{b}^(2) = {100.084}`

• 
  `{b}= √(100.084 \: )`

• 
  `b = 10.0042`

• 
  `b \approx \underline{ \boxed{ \blue{ 10}}}`

Hence, the measures of the longer side/leg is 10 units.

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We can also find the longer leg of the right triangle using the formula

• 
  `\underline{ \boxed{b = √( c²-a² \: )}}`

`\sf \: \bold{ Given: } \: c = 12.21 \: ; \: a=7 \: ; \: b= \: \red ?`

Substitute the given values of a and c to the given formula above, to get the unknown value (b).

• 
  `b = √( c²-a² \: )`

• 
  `b = √( 12.21²-7² \: )`

• 
  `b = 10.0042`

• 
  `b \approx \orange{ 10}`

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