Matematinės stačiojo trikampio formulės
Plotas
S
=
a
⋅
b
2
,
S
=
ρ
⋅
(
ρ
+
2
⋅
r
)
{\displaystyle {\begin{aligned}S&={\frac {a\cdot b}{2}},\\S&=\rho \cdot (\rho +2\cdot r)\end{aligned}}}
Įžambinė
c
=
a
2
+
b
2
,
c
=
a
2
a
2
−
h
c
2
,
c
=
b
2
b
2
−
h
c
2
{\displaystyle {\begin{aligned}c&={\sqrt {a^{2}+b^{2}}},\\c&={\frac {a^{2}}{\sqrt {a^{2}-h_{c}^{2}}}},\\c&={\frac {b^{2}}{\sqrt {b^{2}-h_{c}^{2}}}}\end{aligned}}}
c
=
a
sin
(
α
)
=
b
cos
(
α
)
,
c
=
b
sin
(
β
)
=
a
cos
(
β
)
{\displaystyle {\begin{aligned}c&={\frac {a}{\sin(\alpha )}}={\frac {b}{\cos(\alpha )}},\\c&={\frac {b}{\sin(\beta )}}={\frac {a}{\cos(\beta )}}\end{aligned}}}
Statinis
a
=
c
2
−
b
2
,
a
=
b
⋅
h
c
b
2
−
h
c
2
,
a
=
c
2
⋅
(
c
−
c
2
−
4
⋅
h
c
2
)
{\displaystyle {\begin{aligned}a&={\sqrt {c^{2}-b^{2}}},\\a&={\frac {b\cdot h_{c}}{\sqrt {b^{2}-h_{c}^{2}}}},\\a&={\sqrt {{\frac {c}{2}}\cdot \left(c-{\sqrt {c^{2}-4\cdot h_{c}^{2}}}\right)}}\end{aligned}}}
a
=
c
⋅
sin
(
α
)
=
c
⋅
cos
(
β
)
,
a
=
b
⋅
tan
(
α
)
=
b
⋅
cot
(
β
)
{\displaystyle {\begin{aligned}a&=c\cdot \sin(\alpha )=c\cdot \cos(\beta ),\\a&=b\cdot \tan(\alpha )=b\cdot \cot(\beta )\end{aligned}}}
b
=
c
2
−
a
2
,
b
=
a
⋅
h
c
a
2
−
h
c
2
,
b
=
c
2
⋅
(
c
+
c
2
−
4
⋅
h
c
2
)
{\displaystyle {\begin{aligned}b&={\sqrt {c^{2}-a^{2}}},\\b&={\frac {a\cdot h_{c}}{\sqrt {a^{2}-h_{c}^{2}}}},\\b&={\sqrt {{\frac {c}{2}}\cdot \left(c+{\sqrt {c^{2}-4\cdot h_{c}^{2}}}\right)}}\end{aligned}}}
b
=
c
⋅
cos
(
α
)
=
c
⋅
sin
(
β
)
,
b
=
a
⋅
cot
(
α
)
=
a
⋅
tan
(
β
)
{\displaystyle {\begin{aligned}b&=c\cdot \cos(\alpha )=c\cdot \sin(\beta ),\\b&=a\cdot \cot(\alpha )=a\cdot \tan(\beta )\end{aligned}}}
Perimetras
p
=
a
+
b
+
c
,
p
=
2
⋅
ρ
+
4
⋅
r
{\displaystyle {\begin{aligned}p&=a+b+c,\\p&=2\cdot \rho +4\cdot r\end{aligned}}}
Aukštinės , nubrėžtos į įžambinę, ilgis
h
c
=
a
⋅
b
c
,
1
h
c
2
=
1
a
2
+
1
b
2
{\displaystyle {\begin{aligned}h_{c}&={\frac {a\cdot b}{c}},\\{\frac {1}{{h_{c}}^{2}}}&={\frac {1}{a^{2}}}+{\frac {1}{b^{2}}}\end{aligned}}}
h
c
=
b
⋅
sin
(
α
)
=
a
⋅
cos
(
α
)
,
h
c
=
a
⋅
sin
(
β
)
=
b
⋅
cos
(
β
)
{\displaystyle {\begin{aligned}h_{c}&=b\cdot \sin(\alpha )=a\cdot \cos(\alpha ),\\h_{c}&=a\cdot \sin(\beta )=b\cdot \cos(\beta )\end{aligned}}}
Kampas
α
+
β
=
γ
=
90
∘
{\displaystyle \alpha +\beta =\gamma =90^{\circ }}
α
=
arcsin
(
a
c
)
=
arccos
(
b
c
)
,
α
=
arctan
(
a
b
)
=
arccot
(
b
a
)
{\displaystyle {\begin{aligned}\alpha &=\arcsin \left({\frac {a}{c}}\right)=\arccos \left({\frac {b}{c}}\right),\\\alpha &=\arctan \left({\frac {a}{b}}\right)=\operatorname {arccot} \left({\frac {b}{a}}\right)\end{aligned}}}
β
=
arcsin
(
b
c
)
=
arccos
(
a
c
)
,
β
=
arctan
(
b
a
)
=
arccot
(
a
b
)
{\displaystyle {\begin{aligned}\beta &=\arcsin \left({\frac {b}{c}}\right)=\arccos \left({\frac {a}{c}}\right),\\\beta &=\arctan \left({\frac {b}{a}}\right)=\operatorname {arccot} \left({\frac {a}{b}}\right)\end{aligned}}}
Įbrėžtinio apskritimo spindulys
ρ
=
a
+
b
−
c
2
=
a
⋅
b
a
+
b
+
c
{\displaystyle \rho ={\frac {a+b-c}{2}}={\frac {a\cdot b}{a+b+c}}}
Apibrėžtinio apskritimo spindulys
r
=
c
2
{\displaystyle r={\frac {c}{2}}}
