Step-by-step explanation:
remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides and the associated angles are always opposite of each other.
and ... the sum of all angles in a triangle is always 180°.
sin(90) = 1.
1.
another right-angled triangle.
500/sin(90) = depth/sin(37)
depth = 500×sin(37)/1 = 300.9075116... m
2.
another right-angled triangle.
the ladder is the Hypotenuse (baseline).
the height of the wall and the ground distance are the 2 legs.
the angle we are looking for is opposite of the wall height.
so, we get
14/sin(90) = 13/sin(elevation) = 14
sin(elevation) = 13/14 = 0.928571429...
angle of elevation = 68.2132107...°
3.
both lines are tangents to the circle. so, both distances (from the starting point J to the touching points K and M) must be equal.
so,
5x - 4 = 2x + 2
3x = 6
x = 2
