Respuesta :
The yard is obtuse!
[tex]\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Explanation :-}}}}}}[/tex]
- Determination of acute angled triangle:-When the square of the longest side is less than the sum of the squares of two shorter sides then the triangle is acute angled.
- Determination of right angled triangle:-When the square of the longest side is equal to the sum of the squares of two shorter sides then the triangle is right angled .
- Determination of obtuse angled triangle:-When the square of the longest side is more than the sum of the squares of two shorter sides then the triangle is obtuse angled.
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
Final answer ⤵️
- Longest side = 120 feet
- Shorter side = 85 feet
- Shortest side = 84 feet
[tex] \sf \longrightarrow \: {120}^{2} > {85}^{2} + {84}^{2} [/tex]
[tex] \sf \longrightarrow \:14400> 7225 + 7056[/tex]
[tex] \sf \longrightarrow \:14400> 14281[/tex]
[tex] \qquad \mathbb{TRUE}[/tex]
Thus, The triangle is obtuse angled...~
- a=120
- b=84
- c=85
We need angle
Apply law of cosines
[tex]\\ \rm\Rrightarrow c^2=a^2+b^2-2abcos\gamma[/tex]
[tex]\\ \rm\Rrightarrow 2abcos\gamma=a^2+b^2-c^2[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{a^2+b^2-c^2}{-2ab}[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{120^2+84^2-85^2}{-2(120)(84)}[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{14400+7056-7225}{-20160}[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{14231}{-20160}[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=-0.714[/tex]
[tex]\\ \rm\Rrightarrow \gamma=cos^{-1}(-0.714)[/tex]
[tex]\\ \rm\Rrightarrow \gamma=135.56°[/tex]
The yard is obtuse
