Geometry Trigonometry Review

Front

What is the formula for the area of a sector in a circle?

Back

The area of a sector is given by the formula: \( A = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the angle in degrees and \( r \) is the radius.

Front

How do you calculate the length of an arc in a circle?

Back

The length of an arc is calculated using the formula: \( L = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the angle in degrees and \( r \) is the radius.

Front

What is the relationship between the radius and the arc length in a circle?

Back

The arc length is directly proportional to the radius; as the radius increases, the arc length increases for a given angle.

Front

How do you convert a distance traveled along a circular track into an angle in degrees?

Back

To convert the distance traveled into an angle, use the formula: \( \theta = \frac{L}{r} \times \frac{180}{\pi} \), where \( L \) is the arc length and \( r \) is the radius.

Front

What is the definition of a minor arc in a circle?

Back

A minor arc is the shorter arc connecting two points on a circle, measuring less than 180 degrees.

Front

What is the formula for finding the height of a tower using angles of elevation?

Back

The height of the tower can be found using the formula: \( h = d \tan(\theta) \), where \( d \) is the distance from the observer to the base of the tower and \( \theta \) is the angle of elevation.

Front

What is the tangent function in relation to right triangles?

Back

In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \).

Front

How do you find the missing side of a right triangle using the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse and \( a \) and \( b \) are the other two sides.

Front

What is the significance of rounding answers in geometry problems?

Back

Rounding answers is important for precision and clarity, especially when dealing with measurements; it helps to present answers in a manageable format.

Front

How do you determine the angle of elevation from a point to the top of a tower?

Back

The angle of elevation is determined by measuring the angle formed between the horizontal line from the observer's eye to the top of the tower.