Q) The angles of depression of the top and the bottom of a 8 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between the two buildings. Ans: Step 1: Let’s start with the diagram for this question: Here […]
December 2024
Q) Prove that (√2 + √3)2 is an irrational number, given that √6 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering (√2 + √3)2 is a rational number (by the method of contradiction) If (√2 + √3)2 is a rational number, then it can be expressed in the form of ,
Prove that (√2 + √3)2 is an irrational number, given that √6 is an irrational number. Read More »
Q) Prove that is an irrational number. It is given that √3 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering is a rational number. ∴ = (here p and q are integers and q ≠ 0) ∴ (2 – √3) = 5 ∴ √3 = 2 – 5
Q) A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h. Ans: Step 1: Let’s start with the diagram for this question: Here,
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. Read More »
Q) The angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β, prove that the distance of the cloud from the point of observation is . Ans: Step 1: Let’s draw a diagram for the given
Q) From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given by tan α tan ẞ / (tan α + tan
From an aeroplane vertically above a straight horizontal road, the angles of depression Read More »
Q) From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be a and ẞ. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the
Q) An observer 1.5 m tall is 28.5 m away from a tower and the angle of elevation of the top of the tower from the eye of the observer is 45 degrees. What is the height of the tower? Ans: Step 1: Let’s draw a diagram for the given question: Let the tower be
Q) An observer 1.5 m tall is 28.5 m away from a 30 m high tower. Determine the angle of elevation of the top of the tower from the eye of the observer. Ans: Step 1: Let’s draw a diagram for the given question: Let the tower be AB and observer be CD. We need
Q. Divide the polynomial x3 – 3 x2 + 5 x – 3 by x2 – 2 Ans: To divide the given polynomial, we can write the function as: = = = = = = = = = = = = Therefore, When we divide X3 – 3 X2 + 5 X – 3 by X2
Divide the polynomial x³ – 3x² + 5x – 3 by x² – 2 Read More »