Answer:
Option C) [tex]\tan 60^\circ = \sqrt3[/tex]
Step-by-step explanation:
We are given the following in the question:
A right angled triangle XYZ.
[tex]\angle XZY = 90^\circ\\\angle ZXY = 60^\circ\\\angle XYZ = 30^\circ[/tex]
Length of hypotenuse XY = 42
Length of XZ = 21.
The right angle triangle follows or satisfy the Pythagoras theorem
- The Pythagoras theorem states that the hypotenuse is the longest side of a right angles triangle and that the sum of square of both the sides of the right angles triangle is equal to the square of the hypotenuse.
Thus, we can write:
[tex](\text{Side 1})^2 + (\text{Side 2})^2 = (\text{Hypotenuse})^2[/tex]
Putting the values, we get,
[tex](XZ)^2 + (ZY)^2 = (XY)^2\\(21)^2 + (ZY)^2 = (42)^2\\(ZY)^2 = 1764 - 441 = 1323\\ZY = \sqrt{1323} = 21\sqrt{3}[/tex]
Now, we define,
[tex]\bold{\tan \theta} = \displaystyle\frac{\text{Perpendicular}}{\text{Base}}[/tex]
where the perpendicular and base are in accordance with the angle [tex]\theta[/tex]
Putting the values, we:
[tex]\tan 6 0^\circ = \displaystyle\frac{ZY}{XZ} = \frac{21\sqrt3}{21} = \sqrt3[/tex]
Option C) [tex]\tan 60^\circ = \sqrt3[/tex]
