NIELIT University(Govt. of India Institution) B.Tech/ M.Tech
ApplyLast Date to Apply : 15th September | Campuses in Agartala, Aizawl, Ajmer, Aurangabad, Calicut, Imphal, Itanagar, Kohima, Gorakhpur, Patna & Srinagar
Cosine Rule is considered one of the most asked concept.
18 Questions around this concept.
A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 450. It flies off horizontally straight away from the point O.After one second, the elevation of the bird from O is reduced to 300. Then the speed (in m/s) of the bird is :
The angle of elevation of the top of a vertical tower from a point A, due east of it is 450. The angle of elevation of the top of the same tower from a point B, due south of A is 300. If the distance between A and B is m , then the height of the tower (in metres), is :
Two ships A and B are sailing straight away from a fixed point O along routes such that AOB is always 1200. At a certain instance, OA = 8 km, OB = 6 km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr) :
JEE Main 2025: Sample Papers | Syllabus | Mock Tests | PYQs | Video Lectures
JEE Main 2025 Formula: Physics | Maths | Chemistry
JEE Main 2025: Preparation Guide | High Scoring Topics | Study Plan 100 Days
If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the
tower, are 300, 450 and 600 respectively,then the ratio, AB : BC, is :
Cosine Rule
For a triangle with angles A, B, and C, and opposite corresponding sides a, b, and c, respectively, the Law of Cosines is given as three equations.
Proof:
Drop a perpendicular from C to the x-axis (this is the altitude or height). Recalling the basic trigonometric identities, we know that
In terms of θ, x = bcos θ and y = bsin θ. The (x, y) point located at C has coordinates (bcos θ, bsin θ).
Using the side (x − c) as one leg of a right triangle and y as the second leg, we can find the length of hypotenuse a using the Pythagoras Theorem. Thus,
Now as equals angle A
Similarly we can derice formulae for cosB and cosC
"Stay in the loop. Receive exam news, study resources, and expert advice!"