Geometry

Assuming the triangle to be a right-angled triangle, then use Pythagoras.

h^(2) = (0.024)^(2) + ( 0.007)^(2)

h^(2) = 0.000576 + 0.000049

h^(2) = 0.000625

h = sqrt(0.000625)

h = 0.025 The answer!!!!!

Depending on the information given;-

If two other(shorter) sides are known, use Pythagoras.

h^(2) = a^(2) + b^(2)

If one angle and one side are given then you use Trigonometry .

Sin(angle) = opposite/ hypotenuse

hypotenuse = opposite/Sin(angle)

or

Cos(angle) = adjacent/hypotenuse

hypotenuse = adjacent/ Cos(Angle).

Apply Pythagoras.

11^(2) = 8^(2) + s^(2)

Algebraically rearrange

s^(2) = 11^(2) - 8^(2)

Factor

s^(2) = ( 11 - 8)(11 + 8)

s^(2) = 3(19)

s^(2) = 57

s = sqrt(57)

s = 7.549834435.... ~ 7.55 (2 d.p.).

NB

You can only factor two squared terms when there is a NEGATIVE (-) between them. You CANNOT factor two squared terms with a positive(+) between them.

The HYPOTENUSE is the side of a Right-Angled Triangle, opposite to the 90 degree angle.

It is the LONGEST side of a right angled triangle.

Impossible to tell from the given information.

You need at least the length of the other side , then apply Pythagoras.

or

An angular value and apply trigonometry.

NB You need the length of TWO sides or TWO angles.

For ANY triangle on a 2-dimensional surface ALWAYS add to 180 degrees.

Hence

20 + 90 + x = 180

110 + x = 180

x = 70 The value of the third angle.

To test if a triangle in right angled. apply Pythagorean Formula

H^(2) = s^(2) + S^(2)

H is the hypotenuse and will always be the longest side.

Hence

for a 20, 40 , 80 triangle.

H ; 80^(2) = 6400

s^(2) + S^(2) [ 20^(2) + 40^(2) = 400 + 1600 = 2000

2000 is NOT equal to 6400. Hence for the given dimensions it is NOT a Right-Angled triangle.

Types of triangle ;

EQUILATERAL all three sides the same length and all three angles are 60 degrees.

ISOSCELES Two sides the same length and two angles have the same degrees value.

RIGHT-ANGLED All three sides can be of different lengths. However, it MUST have one Right-Angle (90 degrees)

SCALENE All three sides of different lengths and all three angles of different angular values.

NB In ALL four cases the sum of the interior angles MUST ADD TO 180 DEGREES.

On a plain 2-dimensional surface , then the answer is NO!!!!!

NB. However, on a 3-dimensiobal surface, such as a sphere (Earth), then it is possible to have such a triangle.

OBTUSE (Blunt) is any angle between 90 degrees and 180 degrees.

ACUTE (Sharp) 9s any angle between 9 degrees and 90 degrees.

RIGHT ANGLE is EXACTLY 90 degrees.

The n these is REFLEX angle , which is any angle between 180 degrees and 360 degrees. ( The 'outside' angle of an acute, right-angle, or obtuse angle).

80 degrees is an ACUTE angle

NB

ACUTE angles are LESS THAN 90 degrees

RIGHT ANGLE is exactly 90 degrees

OBTUSE angles are GREATER THAN 90 DEGREES an LESS THAN 180 degrees

STRAIGHT LINE is any point on a straight line is 180 degrees

REFLEX angles are greater than 180 degrees but less than 360 degrees.

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