[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
[tex]\frak{Good\;Morning!!}[/tex]
[tex]\pmb{\tt{Question\;1}}[/tex]
[tex]\star\boldsymbol{\rm{Given-:}}[/tex]
[tex]\star\boldsymbol{\rm{We're\;looking\;for-:}}[/tex]
This is how it's done.
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
There's a special formula that we can use if we need to find the longest side of a right triangle. Fortunately, all of these triangles are right ones! Good.
The formula is. [tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]. This formula is known as Pythagoras' Theorem. This formula only works for right triangles.
Since we have a and b, we can just put in the values (7 for a and 5 for b), And then simplify!
[tex]\boldsymbol{\rm{7^2+5^2=c^2}}[/tex] | 7^2 simplifies to 49, and 5^2 simplifies to 25
[tex]\boldsymbol{\rm{49+25=c^2}}[/tex]. | add
[tex]\boldsymbol{\rm{74=c^2}}[/tex] | square root both sides
[tex]\boldsymbol{\rm{8.6=c}}}[/tex]. | the answer is given to 1 decimal place, as the problem required
[tex]\orange\hspace{350pt}\above5[/tex]
[tex]\pmb{\tt{Question\;2}}[/tex]
Once more, we're given two sides, and asked to find the third one,
which is still the longest side.
[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex] is still the formula used here
Put in 5 for a and 3 for b.
[tex]\boldsymbol{\rm{5^2+3^2=c^2}}[/tex] | 5^2 simplifies to 25, and 3^2 simplifies to 9
[tex]\boldsymbol{\rm{25+9=c^2}}[/tex] | add
[tex]\boldsymbol{\rm{34=c^2}}[/tex] | square root both sides
[tex]\boldsymbol{\rm 5.8=c}}[/tex] | once again it's given to one decimal place
[tex]\hspace{350pt}\above5[/tex]
[tex]\pmb{\tt{Question\;3}}[/tex]
This problem is solved the exact same way
[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]
[tex]\boldsymbol{\rm{8.2^2+4.7^2=c^2}}[/tex]
[tex]\boldsymbol{\rm{67.24+22.09=c^2}}[/tex]
[tex]\boldsymbol{\rm{89.33=c^2}}[/tex]
[tex]\boldsymbol{\rm{9.5=c}}[/tex], rounded to one D.P.
[tex]\orange\hspace{300pt}\above2[/tex]
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
[tex]\pmb{\tt{Question4}}[/tex]
Here we have the longest side and one side length-:
[tex]\boldsymbol{\rm{4^2+b^2=7^2}}[/tex] | 4^2 simplifies to 16 and 7^2 simplifies to 49
[tex]\boldsymbol{\rm{16+b^2=49}}[/tex] | subtract 16 from both sides
[tex]\boldsymbol{b^2=33}[/tex] | square root both sides
[tex]\boldsymbol{\rm{b=5.7}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\pmb{\tt{Question\;5}}[/tex]
[tex]\boldsymbol{\rm{3.8^2+b^2=7.9^2}}[/tex]
[tex]\boldsymbol{\rm{14.44+b^2=62.41}}[/tex]
[tex]\boldsymbol{\rm{b^2=47.97}}[/tex]
[tex]\boldsymbol{\rm{b=6.9}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\pmb{\tt{Question\;6}}[/tex]
[tex]\boldsymbol{\rm{a^2+6.1^2=7.3^2}}[/tex]
[tex]\boldsymbol{\rm{a^2+37.21=53.29}}[/tex]
[tex]\boldsymbol{\rm{a^2=16.08}}[/tex]
[tex]\boldsymbol{\rm{a=4.0}}[/tex]
[tex]\pmb{\tt{done~!!!}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
