Question

In the above triangle, if x = , y = 1, and z = 2, then which of the following is equal to tan(60°)?

A.
`√(3)`
B.
`(√(2) )/(2)`
C.
`(√(3) )/(2)`
D.
`(√(3) )/(3)`

Answer 1

Hello!

The answer is:

The correct option is:

A.
`√(3)`

Why?

Since we already know the hypothenuse and the opposite side of the triangle (y), we can calculate the value of "x" using the Pythagorean Theorem.

We have that:

`Hypothenuse^(2)=Adjacent^(2)+Opposite^(2)`

We know that:

`Hypothenuse=z=2\\Adjacent=x=1`

So, substituting and calculating we have:

`2^(2)=1^(2)+Opposite^(2)`

`4-1=Opposite^(2)`

`Opposite^(2)=3\\Opposite=√(3)`

Then,using the following trigonometric relation:

`Tan(\alpha)=(Opposite)/(Adjacent)\\\\Tan(60\°)=Tan((Opposite)/(Adjacent))=Tan((√(3) )/(1))^=\sqrt{3`

We have that the correct option is:

A.
`√(3)`

Have a nice day!

Answer 2

Answer: Option A

`tan(60\°) = √(3)`

Explanation:

We know the sides and z. So since it is a straight triangle we use the Pythagorean theorem to pull the length of the x side.

`z ^ 2 = x ^ 2 + y ^ 2\\\\x^2 = z^2 - y^2\\\\x=√(z^2 - y^2)\\\\x=√(2^2 - 1^2)\\\\x=√(4 - 1)\\\\x=√(3)`

By definition, the tangent of an angle is:

`tan(\theta) = (opposite)/(adjacent)`

In this case:

`adjacent = y=1\\\\opposite=x =√(3)\\\\\theta=60\°`

Then:

`tan(60\°) = (√(3))/(1)`

`tan(60\°) = √(3)`