if a and b are acute angles (in degrees) such that Csc A = square root of 17 and Csc B = square root of 34/3, what is a+b?

Answer 1

Use the definition of trig functions to determine sin A, sin B, cos A, cos B. Then use for sum formula.

Answer 2

A+B = 45 degrees or pi/4 radians

cscA = sqr17 = 1/sinA

sinA = 1/sqr17 = about 0.2425

A = about 14.037 degrees

cscB = sqr34/3

sinB = 3/sqr34 = about 0.5145

B = about 30.963 degrees

A + B = 14.037 + 30.963 = 45.000 = 45 degrees

cosA = 4/sqr17

cosB = 5/sqr34

sin(A+B) = sinAcosB + cosAsinB

1/sqr17)(5/sqr34) + 4sqr17)(3/sqr34) = 5/17sqr2 + 12/17sqr2 = 17/17sqr2 = 1/sqr2

A+ B = the angle whose sine is 1/sqr2

= 45 degrees or pi/4

that's probably the answer you want, unless by a+b you didn't mean A+B but meant the sides opposite the angles A+B. Then a+b would be 1+1 = 2, if the A+B = 45. Usually lower case letters are for the sides opposite angles represented by upper case letters.