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How do you find the width and length of a rectangle knowing ONLY the diagonal and its angle?
Wiki User
∙ 10y ago
By using the trigonometric ratios of Sine and Cosine.
The diagonal forms the hypotenuse of a right angled triangle with the length and width of the rectangle forming the other two sides of the triangle - the adjacent and opposite sides to the angle. Then:
sine = opposite/hypotenuse → opposite = hypotenuse x sine(angle)
cosine = adjacent/hypotenuse → adjacent = hypotenuse x cosine(angle)
Wiki User
∙ 10y ago
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How do you work out the length of a rectangle with the width and an angle?
It depends on what angle. The main angles of a rectangle are all 90 degrees and knowing that does not help. If however, the angle in question is the angle made by the diagonal with one of the sides, then it is possible to use a basic trigonometric ratio to work out the length. Details will depend on which angle is given.
How do you find the width and length of a rectangle if you only know the diagnol?
If the only known fact is the length of the diagonal then the width and length of the rectangle CANNOT be determined. The diagonal could be that of a square, or of a rectangle that is very long but quite narrow. Consequently at least one more fact is required such as; the dimension of either the length or the width, or the angle that the diagonal makes to the base of the rectangle or even the area of the rectangle.
How to find the area of a rectangle from diagonal?
You need to know more...either the angle or the length of one of the sides.
Sides of a parallelogram are 15 cm and 8 cm. find the length of each diagonal if the larger angle is 100 degrees?
The length of the diagonal which is to opposite of 100⁰ angle is: diagonal length = √[152 + 82 - 2(15)(8)cos 100⁰] diagonal length ≈ 18 The length of the diagonal which is to opposite of 100⁰ angle is: diagonal length =√[152 + 82 - 2(15)(8)cos 80⁰] diagonal length ≈ 16
Which figure does a diagonal always form a angle bisector a rectangle a trapezoid a square or a quadrilateral?
A diagonal always forms an angle bisector in a square. In a rectangle, trapezoid, or any other quadrilateral, a diagonal does not always bisect the angles.
How do you find the diagonal of a rectangle if you know the length and the angle?
You need to use trigonometry cosine (angle) = length/diagonal diagonal = length/cos(angle)
What is the length of a diagonal rectangle with a length of 9 inches and a width of 3 inches?
To find the diagonal length of a rectangle use Pythagoras' theorem for a right angle triangle.
How do you work out the length of a rectangle with the width and an angle?
It depends on what angle. The main angles of a rectangle are all 90 degrees and knowing that does not help. If however, the angle in question is the angle made by the diagonal with one of the sides, then it is possible to use a basic trigonometric ratio to work out the length. Details will depend on which angle is given.
How do you find the width and length of a rectangle if you only know the diagnol?
If the only known fact is the length of the diagonal then the width and length of the rectangle CANNOT be determined. The diagonal could be that of a square, or of a rectangle that is very long but quite narrow. Consequently at least one more fact is required such as; the dimension of either the length or the width, or the angle that the diagonal makes to the base of the rectangle or even the area of the rectangle.
How do you work out the diameter of a rectangle?
The diameter of a rectangle is the same as its diagonal (angle in a semicircle is a right angle). So the diagonal forms a right angled triangle with the diagonal as the hypotenuse and two sides of the rectangle (a length and a breadth) forming the legs of the triangle. If the lengths of the sides of the rectangle are known, a simple application of Pythagoras's theorem given the measure of the diagonal.
How to find the area of a rectangle from diagonal?
You need to know more...either the angle or the length of one of the sides.
Sides of a parallelogram are 15 cm and 8 cm. find the length of each diagonal if the larger angle is 100 degrees?
The length of the diagonal which is to opposite of 100⁰ angle is: diagonal length = √[152 + 82 - 2(15)(8)cos 100⁰] diagonal length ≈ 18 The length of the diagonal which is to opposite of 100⁰ angle is: diagonal length =√[152 + 82 - 2(15)(8)cos 80⁰] diagonal length ≈ 16
Which figure does a diagonal always form a angle bisector a rectangle a trapezoid a square or a quadrilateral?
A diagonal always forms an angle bisector in a square. In a rectangle, trapezoid, or any other quadrilateral, a diagonal does not always bisect the angles.
How do you find the area of a rectangle from diagonal and 1 angle?
The diagonal multiplied by sin(angle) gives one side of the rectangle and the diagonal times cos(theta) gives the other. So the area is (diagonal)2 x cos(theta) x sin(theta).
Is it possible to circumscribe a 90 degree angle rectangle?
Yes and the diameter of the circle will be the diagonal of the rectangle.
Find the area of a rectangle whose diagonal is 10 feet long and makes a 55 degree angle with one of the sides?
A rectangle = LW If the diagonal of length of 10 ft makes a 55⁰ angle with length L, then the length of width W equals to 10 sin 55⁰ ft, and the length of L equals to 10 cos 55⁰ ft. So that A = LW = (10 sin 55⁰ ft)(10 cos 55⁰ ft) ≈ 47 ft2
What kind of triangle does a rectangle make with a diagonal?
right triangle ( triangles with a right angle)
