RIGHT TRIANGLE
Answer:
- [tex] \color{hotpink} \bold{10} [/tex]
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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
- [tex] c {}^{2} = {a}^{2} + {b}^{2} [/tex]
- [tex] {12.21}^{2} = {7}^{2} + {b}^{2} [/tex]
- [tex] {149.0841} = {7}^{2} + {b}^{2} [/tex]
By transposition/adding the additive inverse of 49.
- [tex] {b}^{2} = {149.0841} - 49[/tex]
The difference of 149.0841 - 49 is 100.084
- [tex] {b}^{2} = {100.084}[/tex]
- [tex] {b}= \sqrt{100.084 \: } [/tex]
- [tex] b \approx \underline{ \boxed{ \blue{ 10}}}[/tex]
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
- [tex] \underline{ \boxed{b = \sqrt{ c²-a² \: }}}[/tex]
[tex] \sf \: \bold{ Given: } \: c = 12.21 \: ; \: a=7 \: ; \: b= \: \red ?[/tex]
Substitute the given values of a and c to the given formula above, to get the unknown value (b).
- [tex]b = \sqrt{ c²-a² \: }[/tex]
- [tex]b = \sqrt{ 12.21²-7² \: }[/tex]
- [tex]b \approx \orange{ 10}[/tex]
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