Subject: Mathematics
Book: Maths Mastery
The Law of Cosines extends the Pythagorean theorem to non-right triangles: c² = a² + b² – 2ab cos(C), where C is the angle opposite side c. If you know two sides and the included angle, you can find the third side; or if you know three sides, you can find an angle. For instance, if a=7, b=5, and angle C=60°, then c² = 7² + 5² – 2×7×5×cos(60°)= 49 + 25 – 70×0.5=49 + 25 – 35=39, so c=√39. This formula solves oblique triangles, essential in astronomy, land surveying, or advanced geometry proofs. Grasping the Law of Cosines complements the Law of Sines to solve any general triangle scenario.
What is the greatest common divisor (GCD) of 36 and 48?
View QuestionWhat is the cube of 4?
View QuestionIf a square has a perimeter of 64 cm, what is its area?
View QuestionWhat is the sum of the first 50 positive integers?
View QuestionA man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?
View QuestionWhat is the value of x if log(x) + log(4) = log(32)?
View QuestionThe sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?
View QuestionA square is inscribed in a circle with a radius of 5 cm. What is the area of the square?
View QuestionA man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?
View QuestionIf sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?
View Question