Answer:
87.0°
Step-by-step explanation:
The law of sines can be used to solve this. We have two sides of a triangle and the angle opposite one of them. We want to find the angle opposite the other known side.
In the attached, the triangle is ΔACS. We have side "a" = 9, and side "c" = 10. Angle A is given as 64°. The law of sines tells us ...
sin(C)/c = sin(A)/a
sin(C) = (c/a)sin(A)
C = arcsin((c/a)sin(A)) = arcsin(10/9·sin(64°)) ≈ 87.03°
The ladder makes an angle of about 87° with the ground.
