Geometry

An isosceles triangle is a triangle that has two sides of equal length. A right triangle has an interior angle of 90 degrees. A right isosceles triangle has both characteristics. The 90 degree angle will be the angle formed by the sides of equal length.

An isoceles triangle has two angles that are the same length with the third being different. It can be a right angle or another angle. or it's also called a Right Isosceles triangle.

For right-angled triangles ONLY, use Pythagoras.

Ther Pythagorean Equation. is

h^(2) = side(1)^(2) + side(2) ^(2).

'h' is the hypotenuse. It is the longest side, and ALWAYS opposite the right angle.

Use Trigonometry.

Sine(Angle) = opposite/ hypotenuse => angle = Sin^(-1)[opposite/hypotenuse[

Cosine(angle) = adjacent /hypotenuse => angle = Cos^(-1)[adjacent/hypotenuse]

Tangent(angle) = opposite/adjacent => angle = Tan^(-1)[opposite/adjacent].

These trig. functions are often reduced to SOH,CAH,TOA.

Depending on your calculator the inverse buttons can be

Sin^(-1) or ArcSin

Cos^9-1) = ArcCos

Tan^(-1) = ArcTan

For example. The side lengths are 5,12,13

Hence

Sin(angle) = opposite/hypotenuse = 5/13

Angle = Sin^(-1) [ 5/13]

Angle = 22.61986495.... degrees.

or

Angle ~ 22.6 ( 1.d.p.).

Simillarly for the other angles, but make sure you use the correct Trig. Function.

Use Pythagoras.

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

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

Factor

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

Substitute

b^(2) = (80 ins - 48 inches)(80 ins)( + 48 ins)

b^(2) = (32ins)(128 ins)

b^(2) = 4096 sq. ins

b = sqrt(4096 sq. ins)

b = 64 ins. THe Answer.

NB

For right angled triangles , use Pythagoras

NNB The algebraic rearrangement CAN be factored. From your algebra learning . Two squared terms with a positive (+) between them CANNOT be factored. However, Two squared terms with a negative(-) between them CAN be factored.

NNNB Do NOT forget to 'square root' both sides at the very end.

Use Pythagoras.

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

Hence

h^(2) = 2a^(2)

Since 'a' = 5 inches ; substitute.

Hence

h^(2) = 2(5inches)^(2)

h^(2) = 2(25 sq. inches)

h^(2) = 50sq.inches

h = sqrt(50 sq. ins)

h = 7.071067812... inches.

h ~ 7.1 inches.

Triangles are congruent if they have the same height and base length, which can be established using the Side-Angle-Side (SAS) postulate or the Angle-Side-Angle (ASA) theorem. In the case of triangles REM and DME, if they share a common side and the angles adjacent to that side are equal, then the triangles can be proven congruent.

The cost of constructing a metallurgical plant can vary widely depending on factors such as location, scale, technology, and specific processes involved. Generally, costs can range from tens of millions to several billion dollars. For instance, a small to medium-sized plant might cost between $100 million and $500 million, while larger, more advanced facilities can exceed $1 billion. Additionally, fluctuations in raw material prices, labor costs, and regulatory requirements can further influence the overall investment.

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Yeah I would buy it and give it a try. But probably buy the full version not GD lite

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Projectiles do not always move in a straight line; their paths are typically parabolic due to the influence of gravity. While they may initially follow a straight trajectory when launched, gravity causes them to curve downward as they travel through the air. Additionally, other factors like air resistance and wind can further alter their paths. Thus, while the initial motion may appear linear, the overall trajectory is generally curved.

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