Final:

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Right-angled triangles are used beside trigonometry to solve real-world distance problems, such as the length a ladder of a known length can go up towards a wall if the angle the ladder makes with the ground is also known. This concept also helps determine the flight path the distance traveled from the beginning point and bearing of a plane that travels at a known speed for some hours, turns at a known angle at the same velocity, and continues to fly for a known number of hours.

A sandwich may be formed like a triangle. A staircase makes a right-angled triangle, with its length being the hypotenuse. Also, a right-angled triangle forms when one stands at the top of the tower, observes an oncoming ship and ventures to calculate the distance between the boat and the bottom of the pillar or the angle of elevation from the top.

All the solutions have been prepared in an elaborate and step-by-step manner. You can use these solutions not only for exam preparation but also to complete your assignments and homework.

Our academic experts have optimized the NCERT solutions not only for the board exams but also for competitive exams and olympiads. Calculate the length of the side of the rhombus if the lengths of the diagonals of a rhombus are given as 16 cm and 12 cm. Calculate the distance from the top of the pole to the far end of the shadow if the height of the flag pole is 18 m the length of its shadow is 9.

An equilateral triangle is given with the length of the sides as 8 cm. Determine the length of its altitude.

The ratio of corresponding sides of two similar triangles is 2 : 3. Find the area of the larger triangle if the area of the smaller triangle is given as 48 cm 2. Prove that: Solution:. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower. If the areas of two similar triangles are equal, prove that they are congruent. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area Ch 13 Maths Class 10 Pdf Keywords of the equilateral triangle described on one of its diagonals. Areas of these triangles are in the ratio a 2 : 3 b 4 : 9 c 81 : 16 d 16 : Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

CD Solution:. ABC is an isosceles triangle right angled at C. ABC is an equilateral triangle of side la. Find each of its altitudes. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

A ladder 10 m long reaches a window 8 m above the ground. A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end.

How far from the base of the pole should the stake be driven so that the wire will be taut? An aeroplane leaves an airport and flies due north at a speed of km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of km per hour. Two poles of heights 6 m and 11m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Prove that Solution:. Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides. In the given figure, two chords Ab and CD of a circle intersect each other at the point P when produced outside the circle.

Nazima is fly fishing in a stream. The trip of her fishing rod is 1. Assuming that her string from the trip of the rod to the fly is that, how much string does she have out see the figure? If she pills 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? Two figures having the same shape but not necessarily the same size are called similar figures Two figures having the same shape as well as same size are called congruent figures Note that all congruent figures are similar but the similar figures need not be congruent.

Two polygons of the same number of sides are similar if i their corresponding angles are equal and ii their corresponding sides are in the same ratio or proportion.

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