Advertisements
Advertisements
प्रश्न
The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?
Advertisements
उत्तर
Let AC be the ladder and A be the position of the window which is 8m above the ground.
Now, the ladder is shifted such that its foot is at point D which is 8m away from the wall.
∴ BD = 8m
At this instance, the position of the ladder is DE.
∴ AC = DE
Using Pythagoras theorem in ΔABC,
AC2 = AB2 + BC2
= (8m)2 + (6m)2
= 64m2 + 36m2
= 100m2
= (10m)2
∴ AC = DE = 10m
Using Pythagoras theorem in ΔDBE,
BE2 = DE2 - BD2
⇒ BE2 = (10m)2 - (8m)2
= 100m2 - 64m2
= 36m2
= (6m)2
⇒ BE = 6m
Thus, the required height up to which the ladder reaches is 6m above the ground.
APPEARS IN
संबंधित प्रश्न
Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 50 cm, 80 cm, 100 cm
An aeroplane leaves an airport and flies due north at a speed of 1,000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1,200 km per hour. How far apart will be the two planes after `1 1/2` hours?
In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2BC.BD.
ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.
Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
Find the length diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2.
In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS2 + TQ2 = TP2 + TR2 (As shown in the figure, draw seg AB || side SR and A-T-B)
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
Find the value of (sin2 33 + sin2 57°)
In the given figure, BL and CM are medians of a ∆ABC right-angled at A. Prove that 4 (BL2 + CM2) = 5 BC2.
Triangle ABC is right-angled at vertex A. Calculate the length of BC, if AB = 18 cm and AC = 24 cm.
The sides of a certain triangle is given below. Find, which of them is right-triangle
16 cm, 20 cm, and 12 cm
Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that : 9(AQ2 + BP2) = 13AB2
Find the unknown side in the following triangles
Find the length of the support cable required to support the tower with the floor
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.
Two squares are congruent, if they have same ______.
If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent.
