Advertisements
Advertisements
Question
The foot of a ladder is 6 m away from its 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 top reach?
Advertisements
Solution
Let the height of the top be x m.
In right angled ΔACB,
AC2 = AB2 + BC2 ...[By Pythagoras theorem]
⇒ AB2 = AC2 – BC2
⇒ x2 = (10)2 – (8)2 = 100 – 64
⇒ x = `sqrt(36)`
⇒ x = 6 m
Hence, the height of the top is 6 m.
APPEARS IN
RELATED QUESTIONS
A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.
A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD = ∠BCD = 90o. Calculate the length of AB.
If the sides of the triangle are in the ratio 1: `sqrt2`: 1, show that is a right-angled triangle.
In figure AB = BC and AD is perpendicular to CD.
Prove that: AC2 = 2BC. DC.
In the figure below, find the value of 'x'.
A man goes 10 m due east and then 24 m due north. Find the distance from the straight point.
To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?
The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ = 9 cm, then AB equals ______.
In ∆PQR, PD ⊥ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, prove that (a + b)(a – b) = (c + d)(c – d).
