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What are the equal lengths of an isosceles triangle which has 2 equal base angles of 75 degrees and an area of 100 square cm showing key stages of work?
Wiki User
∙ 10y ago
Formula: 0.5*a*b*sinC = area or 0.5*side2*sinC = area
Apex angle: 180-75-75 = 30 degrees
So: 0.5*side2*sin30 = 100 square cm
Side as subject of the formula: side = square root of (200/sin30) = 20
Therefore: each equal sides of the isosceles triangle are 20 cm in length
Wiki User
∙ 10y ago
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Can you name 3 different triangles with showing the picture?
Three triangles are: scalene, which has three sides of different lengths, isosceles, which has two sides with the same length, and equilateral, which has three sides that are all the same length. In the picture, the scalene triangle is triangle RST, the isosceles triangle is triangle XYZ, and the equilateral triangle is triangle ABC. If two sides or more sides of a triangle have a little line on them, then they are the same length. Click on the related link, "Three Triangles", to see them.
What is the area of a segment enclosed within a sector of a circle that has a radius of 3 cm and an angle of 40 degrees showing work?
The sector must contain an isosceles triangle and so:- Area of sector: 40/360*pi*3*3 = pi Area of triangle: 0.5*3*3*Sin(40 degrees) = 2.892544244 Area of segment: pi-2.892544244 = 0.249 square cm rounded to 3 decimal places
Does a equilateral triangle have right angle?
Only right triangles have right angles. An equilateral triangle though can't have a right angle because all the angles in any type of triangle must add up to 180 degrees. For each angle to be equilateral, they must be 60 degrees, showing that there is no angle at 90 degrees in an equilateral triangle, which would signify that it would be right.
Can you find the dimensions of an isosceles triangle with an area of XII square inches and a height of IV inches showing details of your work?
First find the length of the base: base = area times 2 divided by height base = 12x2/4 = 6 inches An isosceles triangle can be considered as being two right angled triangles joined together. So by halving the length of the base we can use Pythagoras' Theorem to find the hypotenuse: base2+height2 = hypotenuse2 32+42 = 25 square inches. Square root of 25 = 5 inches Therefore the isosceles triangle has two equal sides of V inches and a base of VI inches.
What is the perimeter of an isosceles triangle whose base is 15.96 cm with an area of 84.9072 square cm showing all work and answer?
These are basically the steps: * Use the formula for the area of a triangle to calculate the height. * Use the height and half the base to calculate the lateral sides. Use the Pythagorean Theorem. (It helps to draw a sketch, to visualize the situation.) * Add the three sides to get the perimeter.
Can you name 3 different triangles with showing the picture?
Three triangles are: scalene, which has three sides of different lengths, isosceles, which has two sides with the same length, and equilateral, which has three sides that are all the same length. In the picture, the scalene triangle is triangle RST, the isosceles triangle is triangle XYZ, and the equilateral triangle is triangle ABC. If two sides or more sides of a triangle have a little line on them, then they are the same length. Click on the related link, "Three Triangles", to see them.
What is the area of an isosceles triangle that has two equal sides of 8.75 cm and two equal angles of 63 degrees showing work and final answer to 3 significant figures?
Area: 0.5*8.75*8.75*sin(54 degrees) = 31.0 square cm to 3 significant figures
What is the area of a segment enclosed within a sector of a circle that has a radius of 3 cm and an angle of 40 degrees showing work?
The sector must contain an isosceles triangle and so:- Area of sector: 40/360*pi*3*3 = pi Area of triangle: 0.5*3*3*Sin(40 degrees) = 2.892544244 Area of segment: pi-2.892544244 = 0.249 square cm rounded to 3 decimal places
Does a equilateral triangle have right angle?
Only right triangles have right angles. An equilateral triangle though can't have a right angle because all the angles in any type of triangle must add up to 180 degrees. For each angle to be equilateral, they must be 60 degrees, showing that there is no angle at 90 degrees in an equilateral triangle, which would signify that it would be right.
What is the segment area of a minor chord with an arc of 40 degrees within a circle which has a radius of 9 cm showing work?
There must be an isosceles triangle within the circle and so:- Area of sector: 40/360*pi*9*9 = 9*pi square cm Area of triangle: 0.5*9*9*sin(40 degrees) = 26.03289819 square cm Area of segment: 9*pi-26.03289819 = 2.241435692 square cm or 2.241 to 3 d.p.
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What are the inside angles of an isosceles trapezoid when its smallest angle is one third the size of its biggest angle showing work with explanations?
Let the biggest angle be x:- If: 1/3x+1/3x+x+x = 360 degrees Then: 2x and 2/3x or 8/3x = 360 degrees So: x = 360 divided by 8/3 => 135 degrees Therefore the four angles are: 45+45+135+135 = 360 degrees Note that an isosceles trapezoid is a 4 sided quadrilateral with a pair of opposite parallel lines of diferent lengths and equal length slanted sides with its base angles being equal making its 4 inside angles adding uo to 360 degrees in common with other quadrilaterals.
What is the area of a triangle having dimensions of 29 cm by 21 cm by 20 cm showing work?
Let the sides of the triangle be abc and their opposite angles be ABC Angle C: (21^2 +20^2 -29^2)/(2*21*20) = 90 degrees by the cosine rule Area: 0.5*21*20*sin(90 degrees) = 210 square cm by the area sine rule Alternatively: 0.5*21*20 = 210 square cm because it is a right angle triangle
What is the perimeter and base angles of an isosceles triangle whose base is 9.96 cm with an area of 33.0672 square cm showing work and answers?
Area: 0.5*9.96*height = 33.0672 sq cmHeight: (33.0672*2)/9.96 = 6.64 cmAn isosceles triangle is in effect two right angle triangles joined together at its line of symmetry and in this case have bases of 9.96/2 = 4.98So using Pythagoras: 6.64 squared+4.98 squared = 68.89Square root of 68.89 = 8.3 which is its hypotenusePerimeter therefore is: 8.3+8.3+9.96 = 26.56 cmBase angles: tangent^-1(6.64/4.98) = 53 degrees to nearest degree
Can you find the dimensions of an isosceles triangle with an area of XII square inches and a height of IV inches showing details of your work?
First find the length of the base: base = area times 2 divided by height base = 12x2/4 = 6 inches An isosceles triangle can be considered as being two right angled triangles joined together. So by halving the length of the base we can use Pythagoras' Theorem to find the hypotenuse: base2+height2 = hypotenuse2 32+42 = 25 square inches. Square root of 25 = 5 inches Therefore the isosceles triangle has two equal sides of V inches and a base of VI inches.
What is the perimeter of an isosceles triangle whose base is 15.96 cm with an area of 84.9072 square cm showing all work and answer?
These are basically the steps: * Use the formula for the area of a triangle to calculate the height. * Use the height and half the base to calculate the lateral sides. Use the Pythagorean Theorem. (It helps to draw a sketch, to visualize the situation.) * Add the three sides to get the perimeter.
What is the area of a triangle having dimensions of 7 by 9 by 13 cm whose largest angles is 96 degrees showing and explaining work?
abSinC C being 96 and 7 and 9 being a and b so it would be (7 * 9)*Sin(96) = 62.65487941Improved Answer:-Area of the triangle: 0.5*7*9*sin(96 degrees) = 31.3274397 square cmNote that 96 degrees is the 'included angle' for sides 7 cm and 9 cm because the largest angle of a triangle is opposite its longest side.
