In a right-angled triangle, the length of the side opposite the right angle is 9
3
cm. What is the length of the side opposite to the angle which measures 30
∘
?
- A9cm
- B3
3
cm - C6cm
- D2
9
3
cm
Solution & Step-by-step Explanation
The side opposite the right angle is the hypotenuse of the triangle.
Thus, Hypotenuse=9
3
cm.
Let the angle be θ=30
∘
. We need to find the side opposite to this angle, which is the Perpendicular (P).
Using the trigonometric ratio:
sinθ=
Hypotenuse
Perpendicular
sin30
∘
=
9
3
P
Since sin30
∘
=
2
1
:
2
1
=
9
3
P
P=
2
9
3
cm
Thus, Hypotenuse=9
3
cm.
Let the angle be θ=30
∘
. We need to find the side opposite to this angle, which is the Perpendicular (P).
Using the trigonometric ratio:
sinθ=
Hypotenuse
Perpendicular
sin30
∘
=
9
3
P
Since sin30
∘
=
2
1
:
2
1
=
9
3
P
P=
2
9
3
cm