Question

What is the length of the altitude of the equilateral triangle below

Answer 1

Answer:

F. 12

Step-by-step explanation:

We have been given an image of a triangle and we are asked to find the length of the altitude of our given triangle.

Since we know that altitude of an equilateral triangle splits it into two 30-60-90 triangle.

We will use Pythagoras theorem to solve for the altitude of our given triangle.

$\text{Leg}^2+\text{Leg}^2=\text{Hypotenuse}^2$

Upon substituting our given values in above formula we will get,

$(4\sqrt{3})^2+a^2=(8\sqrt{3})^2$

$16*3+a^2=64*3$

$48+a^2=192$

$48-48+a^2=192-48$

$a^2=144$

Upon taking square root of both sides we will get,

$a=\sqrt{144}$

$a=12$

Therefore, the length of the altitude of our given equilateral triangle is 12 units and option F is the correct choice.

Answer 2

Answer

Find out the altitude of the equilateral triangle .

To proof

By using the trignometric identity.

$tan\theta = \frac{Perpendicular}{base}$

As shown in the diagram

and putting the values of the angles , base and perpendicular

$tan 60^{\circ} = \frac{a}{4\sqrt{3}}$

$tan 60^{\circ} = \sqrt{3}$

solving

$\sqrt{3} = \frac{a}{4\sqrt{3}}$

$a = \sqrt{3}\times 4 \sqrt{3}$

As

$\sqrt{3}\times \sqrt{3} = 3$

put in the above

a = 4 × 3

a = 12 units

The  length of the altitude of the equilateral triangle is 12 units .

Option (F) is correct .

Hence proved