Question

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

Answer 1

Answer: Option A

$tan(60\°) = \sqrt{3}$

Step-by-step 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.

$z ^ 2 = x ^ 2 + y ^ 2\\\\x^2 = z^2 - y^2\\\\x=\sqrt{z^2 - y^2}\\\\x=\sqrt{2^2 - 1^2}\\\\x=\sqrt{4 - 1}\\\\x=\sqrt{3}$

By definition, the tangent of an angle is:

$tan(\theta) = \frac{opposite}{adjacent}$

In this case:

$adjacent = y=1\\\\opposite=x =\sqrt{3}\\\\\theta=60\°$

Then:

$tan(60\°) = \frac{\sqrt{3}}{1}$

$tan(60\°) = \sqrt{3}$

Answer 2

Hello!

The answer is:

The correct option is:

A. $\sqrt{3}$

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:

$2^{2}=1^{2}+Opposite^{2}$

$4-1=Opposite^{2}$

$Opposite^{2}=3\\Opposite=\sqrt{3}$

Then,using the following trigonometric relation:

$Tan(\alpha)=\frac{Opposite}{Adjacent}\\\\Tan(60\°)=Tan(\frac{Opposite}{Adjacent})=Tan(\frac{\sqrt{3} }{1})^=\sqrt{3$

We have that the correct option is:

A. $\sqrt{3}$

Have a nice day!