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A diagonal of a rectangle is inclined to one side of the rectangle at 25o. What is the measure of the acute angle between the diagonals?
- a)25o
- b)40o
- c)50o
- d)55o
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A diagonal of a rectangle is inclined to one side of the rectangle at2...
Since ∠CAB = 25o ∠CAB = 65o
Let diagonals meet at O. ΔOCB is an isosceles triangle.
∴ ∠OBC = 65o
⇒ ∠BOC = 50o
Most Upvoted Answer
A diagonal of a rectangle is inclined to one side of the rectangle at2...
Given Information:
- The diagonal of a rectangle is inclined to one side of the rectangle at 25o.
To Find:
- The measure of the acute angle between the diagonals.
Solution:
1. Understanding the Problem:
- In a rectangle, the diagonals are always equal in length.
- The angle between the diagonals of a rectangle is always 90 degrees.
2. Given Information:
- One diagonal is inclined at an angle of 25o to one side of the rectangle.
3. Finding the Acute Angle:
- Since the diagonals of a rectangle are perpendicular to each other, the angle between them is 90 degrees.
- The diagonal inclined at 25o forms a right triangle with the side of the rectangle.
- The acute angle between the diagonals can be found using trigonometric ratios.
- Let x be the acute angle between the diagonals.
- In the right triangle, sin(x) = opposite/hypotenuse = side of the rectangle/diagonal
- sin(x) = sin(25o)
- x = sin^(-1)(sin(25o))
- x ≈ 50o
Therefore, the measure of the acute angle between the diagonals is approximately 50o. Hence, the correct answer is option 'C'.
- The diagonal of a rectangle is inclined to one side of the rectangle at 25o.
To Find:
- The measure of the acute angle between the diagonals.
Solution:
1. Understanding the Problem:
- In a rectangle, the diagonals are always equal in length.
- The angle between the diagonals of a rectangle is always 90 degrees.
2. Given Information:
- One diagonal is inclined at an angle of 25o to one side of the rectangle.
3. Finding the Acute Angle:
- Since the diagonals of a rectangle are perpendicular to each other, the angle between them is 90 degrees.
- The diagonal inclined at 25o forms a right triangle with the side of the rectangle.
- The acute angle between the diagonals can be found using trigonometric ratios.
- Let x be the acute angle between the diagonals.
- In the right triangle, sin(x) = opposite/hypotenuse = side of the rectangle/diagonal
- sin(x) = sin(25o)
- x = sin^(-1)(sin(25o))
- x ≈ 50o
Therefore, the measure of the acute angle between the diagonals is approximately 50o. Hence, the correct answer is option 'C'.
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