MATH SOLVE

4 months ago

Q:
# In the above triangle, if x = , y = 1, and z = 2, then which of the following is equal to tan(60°)? A. [tex]\sqrt{3}[/tex] B. [tex]\frac{\sqrt{2} }{2}[/tex] C. [tex]\frac{\sqrt{3} }{2}[/tex] D. [tex]\frac{\sqrt{3} }{3}[/tex]

Accepted Solution

A:

Answer: Option A[tex]tan(60\°) = \sqrt{3}[/tex]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.[tex]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}[/tex]By definition, the tangent of an angle is:[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]In this case:[tex]adjacent = y=1\\\\opposite=x =\sqrt{3}\\\\\theta=60\°[/tex]Then:[tex]tan(60\°) = \frac{\sqrt{3}}{1}[/tex][tex]tan(60\°) = \sqrt{3}[/tex]