Application of trigonometry.

eights and Distances

Horizontal Level and Line of Sight

Line of sight is the line drawn from the eye of the observer to the point on the object viewed by the observer.

Horizontal level is the horizontal line through the eye of the observer.

Angle of elevation

The angle of elevation is relevant for objects above horizontal level.
It is the angle formed by the line of sight with the horizontal level.

Angle of depression

The angle of depression is relevant for objects below horizontal level.
It is the angle formed by the line of sight with the horizontal level.

Calculating Heights and Distances

To, calculate heights and distances, we can make use of trigonometric ratios.

Step 1: Draw a line diagram corresponding to the problem.

Step 2: Mark all known heights, distances and angles and denote unknown lengths by variables.

Step 3: Use the values of various trigonometric ratios of the angles to obtain the unknown lengths from the known lengths.

Be More Curious

Measuring the distances of Celestial bodies with the help of trigonomety

Large distances can be measured by the parallax method. The parallax angle is half the angle between two line of sights when an object is viewed from two different positions. Knowing the parallax angle and the distance between the two positions, large distances can be measured.

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Access Answers of Maths NCERT Class 10 Chapter 12 – Areas Related to Circles Class 10 Maths Chapter 12 Exercise: 12.1 (Page No: 230) 1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles. Solution: The radius of the 1st circle = 19 cm (given) ∴ Circumference of the 1st circle = 2π × 19 = 38π cm The radius of the 2nd circle = 9 cm (given) ∴ Circumference of the circle = 2π × 9 = 18π cm So, The sum of the circumference of two circles = 38π + 18π = 56π cm Now, let the radius of the 3rd circle = R ∴ The circumference of the 3rd circle = 2πR It is given that sum of the circumference of two circles = circumference of the 3rd circle Hence, 56π = 2πR Or, R = 28 cm. 2. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. Solution: Radius of 1s

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Access Answers of Maths NCERT Class 10 Chapter 13 – Surface Areas and Volumes Class 10 Maths Chapter 13 Exercise: 13.1 (Page No: 244) 1. 2 cubes each of volume 64 cm 3 are joined end to end. Find the surface area of the resulting cuboid. Answer : The diagram is given as: Given, The Volume (V) of each cube is = 64 cm 3 This implies that a 3 = 64 cm 3 ∴ a = 4 cm Now, the side of the cube = a = 4 cm Also, the length and breadth of the resulting cuboid will be 4 cm each. While its height will be 8 cm. So, the surface area of the cuboid = 2(lb + bh + lh) = 2(8×4 + 4×4 + 4×8) cm 2 = 2(32 + 16 + 32) cm 2 = (2 × 80) cm 2 = 160 cm 2 2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. Answer: The diagram is as follows: Now, the given parameters are: The diameter of the hemisphere = D = 14 cm

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Access Answers of Maths NCERT class 10 Chapter 4 – Quadratic Equations Class 10 Maths Chapter 4 Exercise 4.1 Page: 73 1. Check whether the following are quadratic equations: (i) (x + 1) 2 = 2(x – 3) (ii) x 2 – 2x = (–2) (3 – x) (iii) (x – 2)(x + 1) = (x – 1)(x + 3) (iv) (x – 3)(2x +1) = x(x + 5) (v) (2x – 1)(x – 3) = (x + 5)(x – 1) (vi) x 2 + 3x + 1 = (x – 2) 2 (vii) (x + 2) 3 = 2x (x 2 – 1) (viii) x 3 – 4x 2 – x + 1 = (x – 2) 3 Therefore, the given equation is quadratic equation. 2. Represent the following situations in the form of quadratic equations: (i) The area of a rectangular plot is 528 m 2 . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot. (ii) The product of two consecutive positive integers is 306. We need to find the integers. (iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to fi

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