Geometry Chapter 8 Review (no 8-1, 8-6 & 8-7)

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is opposite the right angle.

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle if the short leg is known?

Back

Multiply the length of the short leg by 2 to find the hypotenuse.

Front

What is the formula to find the height of an object using the angle of elevation?

Back

Height = Distance from the object * tan(angle of elevation).

Front

If a yacht is anchored 90 feet offshore and the angle of elevation to the top of a lighthouse is 26 degrees, how do you find the height of the lighthouse?

Back

Use the formula: Height = 90 * tan(26 degrees).

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

How do you find the length of a missing side in a right triangle?

Back

Use the Pythagorean theorem or trigonometric ratios (sine, cosine, tangent) depending on the information given.

Front

What is the sine of an angle in a right triangle?

Back

Sine of an angle = Opposite side / Hypotenuse.

Front

What is the cosine of an angle in a right triangle?

Back

Cosine of an angle = Adjacent side / Hypotenuse.

Front

What is the tangent of an angle in a right triangle?

Back

Tangent of an angle = Opposite side / Adjacent side.

Front

How do you round a number to the nearest tenth?

Back

Look at the hundredths place; if it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.