Question
Find the height of an equilateral triangle having side 4 cm. ?
✓
Answer
Let $\triangle A B C$ be the given equilateral triangle.
$\therefore \angle B=60^{\circ}$ $\quad$ $\ldots$[Angle of an equilateral triangle]
Let $A D \perp B C, B-D-C$.
In $\triangle A B D, \angle B=60^{\circ}, \angle A D B=90^{\circ}$
$\therefore \angle \mathrm{BAD}=30^{\circ}$ $\quad$ $\ldots$[Remaining angle of a triangle]
$\therefore \triangle \mathrm{ABD}$ is a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle.
$\therefore A D=\frac{\sqrt{3}}{2} A B$ $\quad$ $\ldots$ [Side opposite to $60^{\circ}$ ]
$=\frac{\sqrt{3}}{2} \times 4$
$=2\sqrt{3} \text { units }$
$\therefore$ The height of the equilateral triangle is $2 \sqrt{3}$ units.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Compare the given quadratic equation to the general form and write values of a,b, c : 2m2 = 5m – 5
The following numbers are irrational?
$\sqrt{2}$
→$\sqrt{2}$
Fill in the blanks:
Porbability of a sure event is .....
Porbability of a sure event is .....
If one zero of the polynomial $x^2 - 4x + 1$ is $\big(2+\sqrt3\big),$ write the other zero.
→Classify the following number as rational or irrational:$\sqrt[3]{3}$
→In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then
What is the measure of ∠MRO?
What is the measure of ∠MRO?
State AAA similarity criterion.
For the equation 4x + 5y = 20 find y when x = 0
The following numbers are irrational?
3.142857
3.142857
Fill in the blanks:
For any event E, P(E) + P(not E) = _____.
For any event E, P(E) + P(not E) = _____.