मराठी

Two Poles of Heights 6 M and 11 M Stand Vertically on a Plane Ground. If the Distance Between Their Feet is 12 M; Find the Distance Between Their Tips. - Mathematics

Advertisements
Advertisements

प्रश्न

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m;
find the distance between their tips.

बेरीज

उत्तर

The diagram of the given problem is given below,

We have Pythagoras theorem which states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.
Here, 11 - 6 = 5m            ...( Since DC is perpendicular to BC )
base = 12 cm

Applying Pythagoras theorem we get,
hypotenuse2 = 52 + 122
h2 = 25 + 144
h2 = 169
h = 13

Therefore, the distance between the tips will be 13m.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 13: Pythagoras Theorem [Proof and Simple Applications with Converse] - Exercise 13 (A) [पृष्ठ १५९]

APPEARS IN

सेलिना Concise Mathematics [English] Class 9 ICSE
पाठ 13 Pythagoras Theorem [Proof and Simple Applications with Converse]
Exercise 13 (A) | Q 9 | पृष्ठ १५९

संबंधित प्रश्‍न

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals


Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?


PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.


Which of the following can be the sides of a right triangle?

2.5 cm, 6.5 cm, 6 cm

In the case of right-angled triangles, identify the right angles.


In the given figure, ∆ABC is an equilateral triangle of side 3 units. Find the coordinates of the other two vertices ?


In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF


In triangle ABC, angle A = 90o, CA = AB and D is the point on AB produced.
Prove that DC2 - BD2 = 2AB.AD.


In equilateral Δ ABC, AD ⊥ BC and BC = x cm. Find, in terms of x, the length of AD.


In a rectangle ABCD,
prove that: AC2 + BD2 = AB2 + BC2 + CD2 + DA2.


Find the Pythagorean triplet from among the following set of numbers.

3, 4, 5


Find the Pythagorean triplet from among the following set of numbers.

9, 40, 41


In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED


In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.


If ‘l‘ and ‘m’ are the legs and ‘n’ is the hypotenuse of a right angled triangle then, l2 = ________


From given figure, In ∆ABC, If AC = 12 cm. then AB =?


Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°

∴ ∠BAC = `square`

∴ ∆ABC is 30° – 60° – 90° triangle

∴ In ∆ABC by property of 30° – 60° – 90° triangle.

∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC

∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`

∴ `square` = 6 and BC = `6sqrt(3)`


A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.


The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.


In a right-angled triangle ABC, if angle B = 90°, BC = 3 cm and AC = 5 cm, then the length of side AB is ______.


If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent.


Two poles of 10 m and 15 m stand upright on a plane ground. If the distance between the tops is 13 m, find the distance between their feet.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×