Question

The base of a triangle is twice its hypotenuse, the sine of the angle opposite to its base is

a) Ö3/2, b) 1, c) 1/2, d) Ö3

Answer 1

the answer b= 2h
the angle opposite to its base is a
so sina = b/2h= b/b=1
the answer is b) 1

Answer 2

Option (c) is correct .

The base of a triangle is twice its hypotenuse, the sine of the angle opposite to its base is
`=(1)/(2)`

Explanation:

Given : base = twice its hypotenuse

that is ,

Consider hypotenuse be x then base will be 2x .

Consider the right angled triangle in figure below with right angle at B and base BC.

∠A is the angle opposite to the base.

`\text sinA=(\text Perpendicular)/(\text Hypotenuse)`

`\text sinA=(BC)/(AC)`

`\text sinA=(x)/(2x)`

`\text sinA=(1)/(2)`

Thus, For the base of a triangle is twice its hypotenuse, the sine of the angle opposite to its base is
`=(1)/(2)`