Find the exact value of tan(x+y) if csco= 5/3 and cosy=5/13

-63/16

Step-by-step explanation:

csc x = 5/3

sin x = 3/5

So x is the angle in a 3-4-5 triangle, opposite of the 3.

cos y = 5/13

So y is the angle in a 5-12-13 triangle, opposite of the 12.

tan(x + y) = (tan x + tan y) / (1 − tan x tan y)

tan(x + y) = (3/4 + 12/5) / (1 − (3/4)(12/5))

tan(x + y) = (3/4 + 12/5) / (1 − 9/5)

tan(x + y) = (15 + 48) / (20 − 36)

tan(x + y) = -63/16

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c