Advertisements
Advertisements
Question
The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder?
Advertisements
Solution
Let LN be the ladder of length 15 m that is resting against a wall. Let M be the base of the wall and L be the position of the window.
The window is 9 m above the ground. Now, MN is the distance between the base of the wall and that of the ladder.
In the right-angled triangle LMN, ∠M = 90°. Hence, side LN is the hypotenuse.
According to Pythagoras' theorem,
l(LN)2 = l(MN)2 + l(LM)2
⇒ (15)2 = l(MN)2 + (9)2
⇒ 225 = l(MN)2 + 81
⇒ l(MN)2 = 225 − 81
⇒ l(MN)2 = 144
⇒ l(MN)2 = (12)2
⇒ l(MN) = 12
∴ Length of seg MN = 12 m.
Hence, the distance between the base of the wall and that of the ladder is 12 m.
RELATED QUESTIONS
The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.
In figure, ∠B of ∆ABC is an acute angle and AD ⊥ BC, prove that AC2 = AB2 + BC2 – 2BC × BD
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. 7 cm, 24 cm, 25 cm
ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2
Identify, with reason, if the following is a Pythagorean triplet.
(24, 70, 74)
AD is drawn perpendicular to base BC of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to 1 place of decimal.
In the figure below, find the value of 'x'.
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.
Two circles having same circumference are congruent.
Points A and B are on the opposite edges of a pond as shown in the following figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.
