Two sides of a triangle have lengths a and b, and the angle between them is u. What value of u will maximize the triangle’s area?

Q: Consider an isosceles triangle whose leg measures 2 cm. Let  be the vertex angle (the angle between…

A:

Q: 5. A steel girder 27 feet long is to be moved on rollers along a passageway 8 feet in width and into…

A: Length of steel girder =27ft width of the passage way=8ft Let w be the width which has to be found.…

Q: If the distance from the center of dilation to one line is 9, and the distance from the center of…

A: Given,   The distance from the center of dilation to one line is 9 The distance from the center of…

Q: Two chords of a circle measuring 40 m and 68 m are perpendicular to each other. If the 68-m chord…

A: Topic - circles

Q: Find the area of the largest isosceles triangle that can be inscribed in a circle of radius r=14

A: We will find required as shown below

Q: Using the pigeonhole principle: Given an equilateral triangle with side length of 1 cm, how many…

A: Pigeonhole Principle: If n pigeonholes are occupied by n+1 or more pigeons, then at least one…

Q: A parallelogram has exactly two paris of perpendicular sides True or false ?

A: The rectangle has exactly two pairs of perpendicular sides.

Q: Where should the point:p be chosen on the line segment So as to maximize the angle o ? AB 2

A:

Q: rve, A(0,1) and what Is the length of the sement between the points ?

A:

Q: Find the angle of least positive measure(not equal to the given measure) that is coterminal with 600…

A: Co terminal angles are angles which have their terminal sides in same location when drawn in…

Q: In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the…

A:

Q: d) A trough for holding water is be formed by taking a piece of sheet metal 60 cm wide and folding…

A:

Q: What is the maximum number of right angles a triangle can have in (a) Euclidean geometry? (b)…

A: Given that

Q: If the perimeter of a sector is 4 times its radius then the radius measure of the central angle of…

A: Given that: P = 4R, where P = Perimeter of the sector and R = radius of the circle

Q: 2. A semicircle will be drawn with the unknown side of a triangular lot as its diameter. Calculate…

A: Perimeter of the above image = ?

Q: A window consists of a rectangle surmounted by a semicircle. If the perimeter of the window is 32…

A: Given is the window consists of a rectangle surmounted by a semicircle of perimeter 32ft. Consider…

Q: A window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12…

A:

Q: A triangle has two sides of length 12 and 11. What is the smallest possible whole-number length for…

A: Given data is : A triangle has two sides of length 12 and 11. To find the smallest possible whole…

Q: A rectangle ABCD which measures 18 centimeters by 24 centimeters is folded once perpendicular to…

A:

Q: a right triangle has a hypotenuse of length 2.5 and one leg of length 2. the length of the other…

A: Given, a right triangle has a hypotenuse of length 2.5 and one leg of length 2. To find, the length…

Q: An isosceles triangle has two equal sides of length 15 inches. Find the angle (apex angle) between…

A:

Q: A triangle has two sides of length 12 and 20. What is the smallest possible whole- number length for…

A: Explanation of the solution is given below....

Q: (5) Prove that in an Isosceles triangle, the angle bisector at the apex angle is also the median and…

A:

Q: 4. The line segment that joins the midpoints of the nonparallel sides of a trapezoid is parallel to…

A: A trapezoid is a quadrilateral with one pair of parallel sides. Consider the figure given below:…

Q: A triangle has two sides of length 10 and 20. What is the smallest possible whole- number length for…

A:

Q: A rectangle has dimensions 10 cm by 5 cm. Determine the measures of the angles at the point where…

A:

Q: What value represents the approximate length of x, the distance from the center of the octagon to…

A: Answer is mentioned below

Q: A factory is to be built on a lot measuring 270 ft by 360 ft. A local building code specifies that a…

A: The formula for the area of rectangle is length x width.

Q: A triangle has two sides of length 19 and 17. What is the smallest possible whole- number length for…

A: We know that the sum of any two sides of a triangle is greater than the third side or in other words…

Q: An altitude of an equilateral triangle has length 6\/3 . What is the perimeterof the triangle?

A: An altitude of an equilateral triangle has length 63. What is the perimeterof the triangle?…

Q: A triangle has two sides of length 13 and 9. What is the smallest possible whole- number length for…

A: Given,  A triangle has two sides of length 13 and 9. We need to calculate the length of third side…

Q: Prove If a line is drawn parallel to one side of a triangle to intersect the other two points .The…

A:

Q: A pyramid with a square base area of 100 square inches has its height cut in half, resulting in a…

A: The base area of the given square pyramid is 100 square inches. Then the side of the base of the…

Q: The three sides of a triangle are 5, x, and 8. Give all possible lengths x so that the triangle is…

A:

Q: The lower edge of a mural, 12 feet high, is 6 feet above the observer's eyes. Under the assumption…

A:

Q: A painting in an art gallery has height and is hung so thatits lower edge is a distance d above the…

A:

Q: A triangle has two sides of length 14 and 5. What is the smallest possible whole-number length for…

A: A triangle has two sides of length 14 and 5. What is the smallest possible whole-number length for…

Q: A rhombus has a diagonal of length 10 meters and an area of 100 m2. Find the length of the other…

A:

Q: In the right triangle ABC, AB=2, BC=4, and ED is a line parallel to AB. Find the angle BAD which…

A: The triangle ABC is as follows

Q: A trapezoid of height is 12 meters, has 22 meters lower base, and an area of 180 square meters,…

A: A trapezoid of height is 12 meters, has 22 meters lower base, and an area of 180 square meters,…

Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of the Norman…

A:

Q: In an isosceles right triangle ABC, with the right angle at C, the length of a leg is 20 inches.…

A: If the length of the leg of a right isosceles triangle is x, then the length of the perpendicular…

Q: the diagonals of a convex quadrilateral have lengths of 14cm and 10 cm. What is its area if the…

A:

Q: A rectangle has dimensions 10 cm by 5 cm .Determine the measures of the angles at the point where…

A:

Q: Prove that if two triangles are similar their heights are in the same proportion as their sides.

A:

Q: A straight wire 50 cm long is bent into the shape of an L. What is the shortest possible distance…

A: Given Data: The length of the wire is: l=50 cm   The figure below represents the bent wire.   Let,…

Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of the Norman…

A:

Q: 13. Given two segments with lengths x and y (x not equal to y), what special parallelograms meet the…

A: Given that two segemnts with lengths x and y where x≠yOur Aim is to tell the type of parallelogram…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.