Advertisements
Advertisements
प्रश्न
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `2sqrt(2)` then `l` (AB) = ?
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 = 180° − 90°
∴ 2x = 90°
∴ x = `90^circ/2`
∴ x = 45°
∴ ∠BAC = ∠BCA = 45°
∴ ∆ABC is a 45° – 45° – 90° triangle.
∴ AB = BC = `1/sqrt(2) xx AC` ...[Side opposite to 45°]
= `1/sqrt(2) xx 2sqrt(2)`
∴ `l` (AB) = 2 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 = 7 cm, b = 24 cm and c = 25 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
The sides of triangle is given below. Determine it is right triangle or not.
a = 8 cm, b = 10 cm and c = 6 cm
A man goes 15 metres due west and then 8 metres due north. How far is he from the starting point?
In an isosceles triangle ABC, AB = AC = 25 cm, BC = 14 cm. Calculate the altitude from A on BC.
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?
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 a ΔABC, AB = BC = CA = 2a and AD ⊥ BC. Prove that
(i) AD = a`sqrt3`
(ii) Area (ΔABC) = `sqrt3` a2
∆ABD is a right triangle right-angled at A and AC ⊥ BD. Show that
(i) AB2 = BC × BD
(ii) AC2 = BC × DC
(iii) AD2 = BD × 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?
Determine whether the triangle having sides (a – 1) cm, `2sqrta` cm and (a + 1) cm is a right-angled triangle.
State the converse of Pythagoras' theorem.
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 \[\frac{ar\left( ∆ PBC \right)}{ar\left( ∆ ABC \right)} = \left| \frac{x + y - 2}{7} \right|\]
Find the diagonal of a rectangle whose length is 16 cm and area is 192 sq.cm ?
From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?
Find the height of an equilateral triangle having side 4 cm?
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 ______.
