Question

State if the three side lengths form an acute obtuse or a right triangle

Answer 1

Given three side lengths form an acute obtuse or a right triangle 17, 21, & 28

Check Right triangle

`\begin{gathered} Hyp^2=opp^2+adj^2 \\ 28^2=17^2+21^2 \\ 28^2\text{ = 289 +441} \\ 784\text{ }\\e\text{ 730} \end{gathered}`

Not a Right triangle

An obtuse triangle is a triangle with one obtuse angle and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry.

Not an Obtuse triangle

`\begin{gathered} \sin \text{ A= }(opp)/(hyp) \\ \sin \text{ A = }(17)/(28) \\ A=sin^(-1)\text{ }(17)/(28) \\ A=37.4^0\text{ (less than 90)} \end{gathered}`
`\begin{gathered} \cos \text{ B = }(adj)/(hyp) \\ \cos \text{ B = }(21)/(28) \\ B=cos^(-1)(21)/(28) \\ B=41.4^0\text{ (less than 90)} \end{gathered}`

`\begin{gathered} \tan \text{ C = }(opp)/(adj) \\ \tan \text{ C = }(17)/(21) \\ C=tan^{-1\text{ }}(17)/(21)\text{ } \\ C=38.9^0\text{ (less than 90) } \end{gathered}`

Hence it is acute angle because all angles are less than 90°