Question 1182049
*[illustration cracker.png].

tan 65 = h/x

h = xtan65

tan 40 = h/(x+290)

h= (x+290) *tan40

Therefore 

x*tan65= (x+290) *tan40

x*tan65= x*tan40 + 290 *tan 40

x*tan65-x*tan40 = 290 *tan 40

x(tan 65 - tan 40 ) = 243.34
1.30x = 243.4

x= 243.4/1.3
x=187.23

tan 65 =  h/187.23

h= 401.5 ft
height of explosion