Question

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

Answer 1

Find missing length :

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


Find missing angle A:


`(a)/(\sin(a)) = (c)/(\sin(c))`


`(19)/(\sin(a)) = (38.95)/(\sin(90))`


`\sin(a) = 0.488`


`a = sin^(-1) (0.488)`


`a = 29.2 \textdegree`


Find Missing B:


`(b)/(\sin(b)) = (c)/(\sin(c))`


`(34)/(\sin(b)) = (38.95)/(\sin(90))`


`\sin(b) = 0.873`


`b = sin^(-1)(0.873)`


`b = 60.8 \textdegree`


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