Chapter 8 Review Extra Practice

Front

What is the measure of an angle in a right triangle if the opposite side is 9.4 and the hypotenuse is 10?

Back

The angle can be found using the sine function: sin(θ) = opposite/hypotenuse = 9.4/10. Therefore, θ = sin^(-1)(0.94) ≈ 70.1°.

Front

How do you find the missing angle in a triangle if two angles are known?

Back

Use the triangle sum theorem: The sum of the angles in a triangle is 180°. If you know two angles, subtract their sum from 180° to find the missing angle.

Front

What is the formula to solve for x in a linear equation?

Back

The general form is ax + b = c. To solve for x, isolate it: x = (c - b) / a.

Front

How do you calculate the angle of elevation of a ramp?

Back

Use the tangent function: tan(θ) = opposite/adjacent. For a ramp 11 inches high and 85 inches long, θ = tan^(-1)(11/85) ≈ 7.4°.

Front

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

Back

The sides of a right triangle are related to its angles through trigonometric ratios: sine, cosine, and tangent.

Front

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

Back

Sine is defined as the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

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

Back

Cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

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

Back

Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side: tan(θ) = opposite/adjacent.

Front

How do you find the height of a triangle if the base and angle are known?

Back

Use the formula: height = base * tan(angle).

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a^2 + b^2 = c^2.