One Acute Angle of a right angled triangle is double the other. If the length of its hypotenuse is 10 cm, then its area is:
Answer: (4) None of these
In the right triangle –
One acute angle of a right angled triangles is double the other.
Then the angles are 30 degree and 60 degree.
Sin 30 degree = AC/10
1/2 = AC/10
AC = 10/2
AC = 5 cm
And Cos 30 degree = AB/10
sqrt.3/2 = AB /10
AB = 10 sqrt.3/2
AB = 5 sqrt.3
The area of the triangle = base x height/2
Then the area of the right angle triangle = 5 x 5 sqrt.3/2
= 25sqrt.3/2 cm square.
Hence, the correct answer is 25sqrt.3/2 cm square.