Advertisements
Advertisements
प्रश्न
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `5sqrt(2)`, then what is the height of ∆ABC?
Advertisements
उत्तर
AB = BC ...[Given]
∴ ∠A = ∠C ...[Isosceles triangle theorem]
Let ∠A = ∠C = x ...(i)
In ∆ABC, ∠A + ∠B + ∠C = 180° ...[Sum of the measures of the angles of a triangle is 180°]
∴ x + 90° + x = 180° ...[From (i)]
∴ 2x = 90°
∴ x = `90^circ/2`
∴ x = 45°
∴ ∠A = ∠C = 45°
∴ ∆ABC is a 45° – 45° – 90° triangle.
∴ AB = BC = `1/sqrt(2) xx AC` ...[Side opposite to 45°]
= `1/sqrt(2) xx 5sqrt(2)`
∴ AB = BC = 5 units
∴ The height of ∆ABC is 5 units.
APPEARS IN
संबंधित प्रश्न
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?
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.
The foot of a ladder is 6 m away from a wall and its top reaches a window 8 m above the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its tip reach?
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.
ABCD is a square. F is the mid-point of AB. BE is one third of BC. If the area of ΔFBE = 108 cm2, find the length of AC.
In an isosceles triangle ABC, if AB = AC = 13 cm and the altitude from A on BC is 5 cm, find BC.
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)
In an equilateral ΔABC, AD ⊥ BC, prove that AD2 = 3BD2.
Find the length of the altitude of an equilateral triangle of side 2a cm.
Find the length of each side of a rhombus are 40 cm and 42 cm. Find the length of each side of the rhombus.
Find the side and perimeter of a square whose diagonal is `13sqrt2` cm.
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `2sqrt(2)` then `l` (AB) = ?
A girl walks 200m towards East and then 150m towards North. The distance of the girl from the starting point is ______.
In the given figure, ΔPQR is a right triangle right angled at Q. If PQ = 4 cm and PR = 8 cm, then P is ______.
