okay so this is going to take some time and I'm doing them by the numbers on them, not in the order you put them on here
Question 1: flagpole
angles are 27, 90, and 63 and height is x and hrizontal distance is 12
sin27/12 = sin63/x
x = sin63 / (sin27/12)
x= approx. 23.6
Question 2: eagle and prey
angles are 75, 90, and 15 and horizontal distance is x and height is 300ft
sin15/300 = sin75/x
x = approx. 1,120 ft (c)
Question 3: difference in heights
smaller triangle angles = 51, 90 (those are the only ones you need to know) height is x and hypotenuse is 805
sin90/805 = sin51/x
x= 625.602
larger triangle angles = 54, 90 (again, the only ones you need to know) height is x and hypotenuse is 846
sin90/846 = sin54/x
x=684.428
take the difference = approx. 59 (a)
Question 4: angle of depression of plane
angles = 85, 90, and 5 and height is x and horizontal distance is 4629
sin85/4629 = sin5/x
x=approx. 405 (d)
last one!!!!!!!!
Question 5: shadow of a tree
angle of elevation is x (you also have a 90 degree angle) height is 10 yards and horizontal distance is 14 yards and hypotenuse is y
14^2 + 10^2 = y^2
y= approx. 17.205
sin90/17.205 = sinx/10
x = sin^-1(10(sin90/17.205))
x = approx. 36 (d)
hope this helped