Question

Use the Special Right Triangle to evaluate sin 60°, cos 60° and tan 60°. Your answers should be exact (not a decimal).

A. sin 60 = 1/2, cos 60 = √3/2, tan 60 = √3/3
B. sin 60 = √2/2, cos 60 = √2/2, tan 60 = 1
C. sin 60 = 1, cos 60 = 0, tan 60 = undefined
D. sin 60 = √3/2, cos 60 = 1/2, tan 60 = √3

Answer 1

The correct option is: Option: D

D. sin 60 = √3/2, cos 60 = 1/2, tan 60 = √3

Explanation:

We will draw a right angled triangle with one angle as 60° and the length of the side adjacent to 60° be 1 units and let the hypotenuse of the triangle be 2 units.

Then by using Pythagorean Theorem we get the other leg of the triangle i.e. leg opposite to 60° will be of length √3 units.

Since,

`2^2=1^2+b^2\\\\4-1=b^2\\\\\\b^2=3\\\\\\i.e.\\\\\\b=√(3)\ units`

We know that in a right angled triangle with one angle as θ, the trignometric ratio corresponding to θ is given by:

`\sin \theta=(opposite\ side)/(Hypotenuse)\\\\\\\cos \theta=(adjacent\ side\ or\ base)/(Hypotenuse)\\\\\\\tan \theta=(opposite\ side)/(adjacent\ side\ i.e.\ base)`

Hence, we get:

`\sin \theta=(√(3))/(2)\\\\\\\cos \tehta=(1)/(2)\\\\\\\tan \theta=√(3)`

Answer 2

sin 60 =
`√(3)`/2
cos 60 = 1/2
tan 60 =
`√(3)`

The answer to your question is D. I hope that this is the answer that you were looking for and it has helped you.