A, b and c are the sides of a right triangle, where side a is across from angle a, side b is across from angle b, and side c is across from the right angle. if a=19 and b=34∘, find the missing sides and angles in this right triangle

Find missing length :

a² + b² = c²
c² = 19² + 34²
c² = 1517
c = √1517
c = 38.95 units.


Find missing angle A:

[tex] \dfrac{a}{\sin(a)} = \dfrac{c}{\sin(c)} [/tex]

[tex] \dfrac{19}{\sin(a)} = \dfrac{38.95}{\sin(90)} [/tex]

[tex]\sin(a) = 0.488[/tex]

[tex]a = sin^{-1} (0.488)[/tex]

[tex]a = 29.2 \textdegree[/tex]


Find Missing B:

[tex] \dfrac{b}{\sin(b)} = \dfrac{c}{\sin(c)} [/tex]

[tex]\dfrac{34}{\sin(b)} = \dfrac{38.95}{\sin(90)}[/tex]

[tex]\sin(b) = 0.873[/tex]

[tex]b = sin^{-1}(0.873)[/tex]

[tex]b = 60.8 \textdegree[/tex]


Answer: Missing length =  38.95 units ; Missing angles =  29.2°  and  60.8°