Unit 4 Retest

Front

What is the length of the sides of an equilateral triangle if the altitude is given?

Back

In an equilateral triangle, the altitude divides the triangle into two 30-60-90 triangles. If the altitude (h) is known, the length of a side (s) can be calculated using the formula: s = 2h/√3.

Front

What is the relationship between the angle of elevation and the height of an object?

Back

The angle of elevation is the angle formed by the horizontal line and the line of sight to an object above the horizontal. The height can be calculated using trigonometric functions, specifically: height = distance * tan(angle of elevation).

Front

How do you find the length of the diagonal in a rectangle?

Back

The length of the diagonal (d) can be found using the Pythagorean theorem: d = √(length² + width²).

Front

What is the formula to calculate the angle formed by the diagonal and a side of a rectangle?

Back

The angle (θ) can be calculated using the cosine function: cos(θ) = adjacent side / diagonal.

Front

How do you calculate the length of a side of a square given its diagonal?

Back

The length of a side (s) can be calculated using the formula: s = diagonal / √2.

Front

What is the significance of the 30-60-90 triangle in relation to equilateral triangles?

Back

In a 30-60-90 triangle, the ratios of the lengths of the sides are 1:√3:2. This relationship helps in finding the lengths of sides in equilateral triangles when the altitude is known.

Front

What is the formula for the area of a triangle?

Back

The area (A) of a triangle can be calculated using the formula: A = 1/2 * base * height.

Front

How do you determine the height of a kite using the angle of elevation?

Back

To find the height (h) of the kite, use the formula: h = distance * sin(angle of elevation).

Front

What is the relationship between the sides of a right triangle and the angles?

Back

In a right triangle, the side opposite the largest angle is the longest side (hypotenuse), and the lengths of the sides are related by the sine, cosine, and tangent functions.

Front

What is the definition of an equilateral triangle?

Back

An equilateral triangle is a triangle in which all three sides are of equal length and all three angles are equal (each measuring 60 degrees).