Explanation

An equilateral triangle has all three sides and angles equal (each angle = 60°).

It is commonly used in geometry and structural design for uniform load distribution.

A scalene triangle has no equal sides and no equal angles.

All sides and angles are of different lengths and measures.

Explanation

Acute angles measure less than 90 degrees.

Right angles measure 90 degrees.

Obtuse angles measure more than 90 degrees.

Explanation

For a parabola with base b and height h, the area is calculated as A = 1/3 × b × h.

This formula comes from integration of the parabolic curve or using the method of exhaustion.

Explanation

The volume of a cube is given by:

V = side³

= 5³

= 5 × 5 × 5

= 125 cm³

Explanation

Given (Sinθ + Cosθ) / (Sinθ - Cosθ) = 4/5

Let’s call this ratio R = 4/5.

We can write:

R = (Sinθ + Cosθ) / (Sinθ - Cosθ)

Multiply numerator and denominator by (Sinθ - Cosθ):

R = [(Sinθ + Cosθ)(Sinθ - Cosθ)] / (Sinθ - Cosθ)²

But better approach is:

Square both numerator and denominator:

R² = (Sinθ + Cosθ)² / (Sinθ - Cosθ)²

Calculate numerator:

(Sinθ + Cosθ)² = Sin²θ + 2SinθCosθ + Cos²θ = 1 + 2SinθCosθ

Denominator:

(Sinθ - Cosθ)² = Sin²θ - 2SinθCosθ + Cos²θ = 1 - 2SinθCosθ

So,

R² = (1 + 2SinθCosθ) / (1 - 2SinθCosθ)

Given R = 4/5, so R² = 16/25

Set:

16/25 = (1 + 2SinθCosθ) / (1 - 2SinθCosθ)

Cross-multiplied:

16(1 - 2SinθCosθ) = 25(1 + 2SinθCosθ)

16 - 32SinθCosθ = 25 + 50SinθCosθ

Bring terms together:

-32SinθCosθ - 50SinθCosθ = 25 -16

-82SinθCosθ = 9

SinθCosθ = -9/82

Now, Tan²θ = (Sin²θ) / (Cos²θ)

Recall identity:

Tan²θ + 1 = sec²θ

and

(Tan²θ + 1) / (Tan²θ - 1) is the required expression.

This requires more complex steps, but the given answer is 41/40.