Explanation:
24.
AC = 12 = cos(angle) × AB = cos(angle) × 13
imagine a circle with center in A and radius 13.
that is why we can say AC = cos(angle) × radius, and BC = sin(angle) × radius.
cos(angle) = 12/13 = 0.923076923...
angle = 22.61986495...°
so, B is the right answer.
25.
we have a right-angled triangle.
from the point in the ground, where the ladder starts, to the point on the wall, where the ladder ends, and the point on the ground right under the wall point.
at this ground point there is the right angle.
at the ladder ground point we have 70°.
so, the angle at ladder/wall point is
180 - 90 - 70 = 20°.
remember, the sum of all angles in a triangle is always 180°.
the ladder itself (20 ft) is the Hypotenuse (the baseline opposite of the 90° angle).
the height of the ladder/wall point is one leg (and what we need to calculate), and the ground distance from the ladder/ground point to the point right under the ladder/wall point is the second leg.
we can use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with the sides being always opposite of the associated angles.
so, we have
20/sin(90) = 20/1 = 20 = height/sin(70)
height = 20×sin(70) = 18.79385242... ft
so, D is the right answer.