Answer:
C: tan 60 = √3
Explanation:
Let the adjacent part of the triangle be x and let the opposite side be y.
Thus, from trigonometric ratios;
x/10 = cos 60
We are given cos 60 = ½
Thus;
x/10 = ½
x = ½ × 10
x = 5
Similarly;
y/10 = sin 60
Now,from trigonometric relationship we know that; sin 60 = cos 30. Thus;
y/10 = cos 30
We are given cos 30 = (√3)/2
Thus;
y/10 = (√3)/2
y = 10 × (√3)/2
y = 5√3
Since it is a right angle triangle with one angle being 60°, it means the other one is 30° since sum of angles in a triangle is 180°.
Thus;
5/(5√3) = tan 30°
1/√3 = tan 30
Similarly;
5/10 = sin 60°
sin 60° = ½
Also;
tan 60 = (5√3)/5
tan 60 = √3
Also;
sin 30 = 5/10
sin 30 = ½
Looking at the options, the only correct one is Option C