Advertisements
Advertisements
Question
Find the height of an equilateral triangle having side 4 cm?
Advertisements
Solution
Let ∆ABC be the given equilateral triangle.
∴ ∠B = 60° ...[Angle of an equilateral triangle]
Let AD ⊥ BC, B – D – C.
In ∆ABD, ∠B = 60°, ∠ADB = 90°
∴ ∠BAD = 30° ...[Remaining angle of a triangle]
∴ ∆ABD is a 30° – 60° – 90° triangle.
∴ `AD = sqrt(3)/2 AB` ...[Side opposite to 60°]
= `sqrt(3)/2 xx 4`
= `2sqrt(3)` units
∴ The height of the equilateral triangle is `2sqrt(3)` units.
APPEARS IN
RELATED QUESTIONS
The sides of triangle is given below. Determine it is right triangle or not.
a = 7 cm, b = 24 cm and c = 25 cm
The sides of triangle is given below. Determine it is right triangle or not.
a = 9 cm, b = l6 cm and c = 18 cm
A man goes 15 metres due west and then 8 metres due north. How far is he from the starting point?
Using Pythagoras theorem determine the length of AD in terms of b and c shown in Figure.
A triangle has sides 5 cm, 12 cm and 13 cm. Find the length to one decimal place, of the perpendicular from the opposite vertex to the side whose length is 13 cm.
The lengths of the diagonals of a rhombus are 24 cm and 10 cm. Find each side of the rhombus.
In the given figure, ∠B < 90° and segment AD ⊥ BC, show that
(i) b2 = h2 + a2 + x2 - 2ax
(ii) b2 = a2 + c2 - 2ax
In a quadrilateral ABCD, ∠B = 90°, AD2 = AB2 + BC2 + CD2, prove that ∠ACD = 90°.
∆ABD is a right triangle right-angled at A and AC ⊥ BD. Show that
(i) AB2 = BC x BD
(ii) AC2 = BC x DC
(iii) AD2 = BD x CD
(iv) `"AB"^2/"AC"^2="BD"/"DC"`
An aeroplane leaves an airport and flies due north at a speed of 1000km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after 1 hours?
State Pythagoras' theorem.
If D, E, F are the respectively the midpoints of sides BC, CA and AB of ΔABC. Find the ratio of the areas of ΔDEF and ΔABC.
ΔABC ~ ΔDEF such that ar(ΔABC) = 64 cm2 and ar(ΔDEF) = 169 cm2. If BC = 4 cm, find EF.
In an equilateral triangle with side a, prove that area = `sqrt(3)/4 a^2`.
The co-ordinates of the points A, B and C are (6, 3), (−3, 5) and (4, −2) respectively. P(x, y) is any point in the plane. Show that \[\frac{ar\left( ∆ PBC \right)}{ar\left( ∆ ABC \right)} = \left| \frac{x + y - 2}{7} \right|\]
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `2sqrt(2)` then `l` (AB) = ?
Find the altitude of an equilateral triangle of side 8 cm.
In the given figure, ΔPQR is a right triangle right angled at Q. If PQ = 4 cm and PR = 8 cm, then P is ______.
