Advertisements
Advertisements
प्रश्न
Find the height of an equilateral triangle having side 4 cm?
Advertisements
उत्तर
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
संबंधित प्रश्न
Construct a triangle ABC with sides BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are `3/4` times the corresponding sides of ∆ABC.
The sides of triangle is given below. Determine it is right triangle or not.
a = 9 cm, b = l6 cm and c = 18 cm
The sides of triangle is given below. Determine it is right triangle or not.
a = 1.6 cm, b = 3.8 cm and c = 4 cm
A ladder 17 m long reaches a window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.
Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
In a ΔABC, AB = BC = CA = 2a and AD ⊥ BC. Prove that
(i) AD = a`sqrt3`
(ii) Area (ΔABC) = `sqrt3` a2
In an acute-angled triangle, express a median in terms of its sides.
Calculate the height of an equilateral triangle each of whose sides measures 12 cm.
In right-angled triangle ABC in which ∠C = 90°, if D is the mid-point of BC, prove that AB2 = 4AD2 – 3AC2.
In the following figure, D is the mid-point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that:
(i) `b^2 = p^2 + ax + a^2/4`
(ii) `c^2 = p^2 - ax + a^2/4`
(iii) `b^2 + c^2 = 2p^2 + a^2/2`
In ∆ABC, ∠A is obtuse, PB ⊥ AC and QC ⊥ AB. Prove that:
(i) AB ✕ AQ = AC ✕ AP
(ii) BC2 = (AC ✕ CP + AB ✕ BQ)
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 the converse of Pythagoras' theorem.
A man goes 12 m due south and then 35 m due west. How far is he from the starting point?
From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `2sqrt(2)` then `l` (AB) = ?
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `5sqrt(2)`, then what is the height of ∆ABC?
A girl walks 200m towards East and then 150m towards North. The distance of the girl from the starting point is ______.
