Explanation:
for what question ?
just in case, always remember Pythagoras
c² = a² + b²
with c being the Hypotenuse, a and b are the legs.
then there is the law of sine
a/sin(A) = b/sin(B) = c/sin(C)
a,b,c being the sides opposite of the A, B, C angles.
and as always : the sum of all angles in a triangle is always 180°.
1.
a)
angle A = 180 - 90 - 35 = 55°
a/sin(55) = 15/sin(90) = 15
a = 15×sin(55) = 12.28728066... m
b)
angle A = 180 - 90 - 25 = 65°
250/sin(65) = b/sin(90) = b = 275.8444797...
2.
a)
remember the trigonometric triangle with the up/down leg being sine (multiplied by the circle radius, which is the Hypotenuse of the triangle), and the left/ right leg being cosine (again multiplied by the Hypotenuse).
5 = 12×sin(x)
sin(x) = 5/12 = 0.416666666...
x = 24.62431835...°
b)
the same principle as for a), just now we need cosine.
12 = 15×cos(x)
cos(x) = 12/15 = 4/5 = 0.8
x = 36.86989765...°
3.
AB² = 125² + 65² = 15625 + 4225 = 19850
AB = sqrt(19850) = 140.890028... cm
angel C = 90°
125/sin(B) = 65/sin(A) = 140.890028.../sin(90)
sin(B) = 125/140.890028... = 0.887216801...
angle B = 62.52556837...°
angle A = 180 - 90 - 62.52556837... = 27.47443163...°