In a triangle, the length of the side opposite the angle which measures 60
∘
is 6cm. What is the length of the side opposite to the angle which measures 90
∘
?
- A3
3
cm - B6cm
- C4
3
cm - D2
9
3
cm
Solution & Step-by-step Explanation
This is a standard right-angled triangle (or we can apply the Law of Sines). Let the side opposite to 60
∘
be a=6cm and the side opposite to 90
∘
(hypotenuse) be c.
Using the sine rule:
sin60
∘
a
=
sin90
∘
c
Substitute the known values:
2
3
6
=
1
c
c=
3
12
Rationalizing the denominator:
c=
3
×
3
12×
3
=
3
12
3
=4
3
cm
Therefore, the length of the side opposite to the 90
∘
angle is 4
3
cm.
∘
be a=6cm and the side opposite to 90
∘
(hypotenuse) be c.
Using the sine rule:
sin60
∘
a
=
sin90
∘
c
Substitute the known values:
2
3
6
=
1
c
c=
3
12
Rationalizing the denominator:
c=
3
×
3
12×
3
=
3
12
3
=4
3
cm
Therefore, the length of the side opposite to the 90
∘
angle is 4
3
cm.