###### Asked in Math and ArithmeticAlgebraGeometry

Math and Arithmetic

Algebra

Geometry

# What is the largest angle of a triangle with sides of 8.5 cm by 14 cm by 9 cm?

## Answer

###### Wiki User

###### June 24, 2017 11:39AM

The largest angle will be opposite the biggest side which is 14 cm and so by using the cosine rule its angle works out as 106.23 degrees rounded to two decimal places.

## Related Questions

###### Asked in Math and Arithmetic, Algebra, Geometry

### What is the largest angle in and area of a triangle with sides of 14 cm by 9 cm by 8.5 cm?

Using the cosine rule the angle can be found:
Largest angle is opposite largest side
→ A = arc cos ((14² - 9² - 8.5²)/(2 × 9 × 8.5)) ≈ 73.8°
For the area, use Heron's formula
Let S = half the perimeter = ½(14 + 9 + 8.5) = 15.75
Area = √(s(s - a)(s - b)(s - c))
= √(15.75 × (15.75 - 14) × (15.75 - 9) × (15.75 - 8.5))
≈ 36.73 sq cm.
Alternatively, you can use the Sine ratio on the largest angle and
the two shorter sides:
area ≈ ½ × 9 × 8.5 × sin 73.8 ≈ 36.73 sq cm
Another Answer: The largest angle of the
triangle is 106.23 degrees and its area is 36.73 square cm both
rounded to two decimal places

###### Asked in Math and Arithmetic, Algebra, Geometry

### If an isosceles triangle has two equal sides that are 14 feet long and the third side is 17 feet long what are the angles?

Let the Isosceles Triangle be ∆ ABC with sides AB = AC = 14',
and BC = 17'
Draw a line bIsecting angle BAC. This line will be perpendicular
to and bisect BC at point D.
Then ∆ DBA (or ∆ DCA) is a right angled triangle with AB the
hypotenuse.
Angle ABD = Angle ABC is one of the two equal angles of the
isosceles triangle.
Cos ABD = BD/AB = 8.5/14 = 0.607143, therefore Angle ABC =
52.62°
The third angle of the triangle is 180 - (2 x 52.62) = 180 -
105.24 = 74.76°
The angles are therefore 52.62° , 52.62° and 74.76° .

###### Asked in Math and Arithmetic, Algebra, Geometry

### What are a score or more facts about the properties of a triangle?

1 It's a 3 sided 2 dimensional polygon
2 It has no diagonals
3 Its largest side is less the sum of its smaller sides
4 Its 3 interior angles add up to 180 degrees
5 Its 3 exterior angles add up to 360 degrees
6 It will tessellate leaving no gaps or overlaps
7 It has a perimeter which is the sum of its 3 sides
8 It has an area which is 0.5*base*perpendicular altitude
9 It can form the base of a tetrahedron pyramid
10 It is the 1st building block of all other polygons
11 It has 3 vertices which is the plural of vertex
12 It's a right angle triangle when it has a 90 degree angle
13 It's an obtuse triangle when it has an obtuse angle and 2
different acute angles
14 It's a scalene triangle when it has 3 different acute
angle
15 It's an equilateral triangle when it has 3 equal sides
16 It's an isosceles triangle when it has 2 equal sides
17 It's subject Pythagoras' theorem as a right angle
triangle
18 It's subject to the rules of trigonometry
19 Its tangent ratio is: opp/adj as a right angle triangle
20 Its sine ratio is: opp/hyp as a right angle triangle
21 Its cosine ratio is: adj/hyp as a right angle triangle
22 Its hypotenuse squared is equal to the sum of its squared
sides as right angle triangle

###### Asked in Math and Arithmetic, Geometry, Trigonometry

### What are a score or more facts and features of a triangle and its properties?

1 It's a 3 sided polygon which means many sides
2 Its sum of its 2 smaller sides is greater than its longest
side
3 It has no parallel sides
4 It has no diagonals
5 It has 3 interior angles that add up to 180 degrees
6 It has 3 exterior angles that add up to 360 degrees
7 It can be a scalene triangle
8 It can be an obtuse triangle
9 It can be an isosceles triangle
10 It can be an equilateral triangle
11 Its longest length is opposite to its largest angle
12 Its hypotenuse is its largest length as a right angle
triangle
13 It brought fame to the ancient Greek mathematician
Pythagoras
14 Its hypotenuse when square is equal to the sum of its squared
sides
15 Its smallest angle is opposite to its shortest side
16 It will tessellate leaving no gaps or overlaps
17 It's a right angle triangle when it has a 90 degree angle and
2 acute angles
18 It can be both an isosceles triangle and a right angle
triangle
19 It has a perimeter which is the sum of its 3 sides
20 It has an area which is: 0.5*base*perpendicular altitude
21 Its area is also: 0.5*a*b*sin(A) whereas a and b are sides
and A is included angle
22 It's subjected to the rules of trigonometry
23 It's the 1st and foremost building block of other
polygons
24 Its 3 corners are vertices which is plural for vertex
25 It has 1 line of symmetry as an isosceles triangle
26 It has 3 lines of symmetry as an equilateral triangle
27 It has rotational symmetry to the order of 3 as an
equilateral triangle
28 it's a 2 dimensional shape
29 It can be the base of a 3 dimensional pyramid
30 It can be doubled up to form a 4 sided quadrilateral

###### Asked in Math and Arithmetic, Algebra, Geometry

### Is it possible to draw a right triangle with the following side length 4 in 10in and 14 in show work?

No, it is impossible to draw any triangle with those side
lengths:
For a triangle to exist the sum of the shorter sides must
exceed (ie be greater than) the longest sides.
The sum of the shorter sides is 4 in + 10 in = 14 in which is
the same as the longest side; thus those sides cannot form any
triangle.

###### Asked in Geometry, Math and Arithmetic, Algebra

### If one angle of a triangle is 14 degrees more than one of the others which is itself 4 degrees more than the smallest one then what is the are the angles of this triangle?

Given that the angles in a triangle will always add up to 180°,
we can say:
a + (a - 14°) + (a - 14° - 4°) = 180°
where "a" represents the largest angle.
∴ 3a - 32° = 180°
∴ 3a = 212°
∴ a = 70 2/3
The other two angles can be calculated by subtracting 14 and 4
degrees, giving us 70 and two thirds, 56 and two thirds, and 52 and
two thirds.

###### Asked in Math and Arithmetic, Algebra, Geometry

### What are a score or more facts about the triangle and its properties?

1 It's a 3 sided 2 dimensional shaped polygon
2 It has no diagonals
3 Its largest side is less than the sum of its smaller sides
4 Its 3 interior angles add up to 180 degrees
5 Its 3 exterior angles add up to 360 degrees
6 It will tessellate leaving no gals or overlaps
7 It has a perimeter which is the sum of its 3 sides
8 It has an area which is: 0.5*base*perpendicular altitude
9 It's the 1st building block of all other polygons
10 It can form the base of a 3 dimensional pyramid
11 It has 3 vertices which is the plural of vertex
12 It's a right angle triangle when it has a 90 degree angle
13 It's an obtuse triangle when it has an angle greater than 90
degrees
14 It's a scalene triangle when it has 3 different acute
angles
15 It's an equilateral triangle when it has 3 equal 60 degree
angles
16 It is an isosceles triangle when it has 2 equal sides
17 It's subject to the rules of trigonometry
18 It's subject to Pythagoras' theorem as a right angle
triangle
19 Its tangent ratio is: opp/adj as a right angle triangle
20 It sine ratio is: opp/hyp as a right angle triangle
21 Its cosine ratio is: adj/hyp as a right angle triangle
22 Its hypotenuse squared is equal to the sum of its squared
sides as right triangle
23 Its properties were well known by the ancient Greeks and
Egyptians
24 It can form the cross-section of a triangular prism
25 It has certain cyclic properties within a circle

###### Asked in Math and Arithmetic, Algebra, Geometry

### If the interior angle of a regular polygon is 13 times the size of a diagnol angle - how many sides does the polygon have?

The interior angle (A) of a regular polygon is bisected by a
diagonal. Therefore two diagonals and one side form an isosceles
triangle with two base angles each measuring ½ A. The diagonal
angle (at the centre) is thus 180 - A.
We then have A = 13(180 -A) : A = 180 x 13/14
The sum of the interior angles of a regular polygon = 2n - 4
right angles = 90(2n - 4)° where n is the number of sides.
Each interior angle (A) = 90(2n - 4) ÷ n = 180 x 13/14 : 180n -
360 = 180n x 13/14 : 180n/14 = 360 : n = 14 x 360/180 = 28
The polygon has 28 sides.