What is the value of tan(60°)? One-half StartRoot 3 EndRoot StartFraction StartRoot 3 EndRoot Over 2 EndFraction StartFraction 1 Over StartRoot 3 EndRoot EndFraction

Question

asked Nov 23, 2021 125k views

2 Answers

Laurens Rietveld · Answer 1 · 2021-11-28T06:10:27+0000

Answer:

$\sqrt3$

Explanation:

To find:

The value of
$tan60^\circ$ = ?

Solution:

Kindly consider the equilateral
$\triangle ABC$ as attached in the answer area.

Let the side of triangle =
units

Let us draw the perpendicular from vertex A to side BC.

It will divide the side BC in two equal parts.

i.e. BD = DC =
(a)/(2)

Using Pythagorean Theorem in
$\triangle ABD$ :

$\text{Hypotenuse}^(2) = \text{Base}^(2) + \text{Perpendicular}^(2)$

Side AD =
$(\sqrt3)/(2)a$

Using Trigonometric ratio:

$tan\theta = (Perpendicular)/(Base)$

tanB = (AD)/(BD)

Putting the values of AD and BD:

$tan60^\circ=((\sqrt3)/(2)a)/((1)/(2)a)\\\Rightarrow tan60^\circ = \bold{\sqrt3}$