Q1. Two sides of a right triangle ABC (C is the right angle) are given: a = 2 and b = 3. Find sin(A). Give the exact answer with a rational denominator.

Background

Topic: Right Triangle Trigonometry

This question tests your understanding of how to use the definitions of trigonometric ratios in a right triangle, specifically the sine function.

Key Terms and Formulas:

• Opposite side: The side opposite the angle in question (here, angle A).

• Hypotenuse: The longest side of a right triangle, opposite the right angle.

• Pythagorean Theorem:

Step-by-Step Guidance

1. Identify which sides correspond to a, b, and c. Typically, in triangle ABC with right angle at C, sides a and b are the legs, and c is the hypotenuse.

2. Use the Pythagorean Theorem to find the length of the hypotenuse: .

3. Determine which side is opposite angle A (it will be side b if A is at vertex A).

4. Set up the sine ratio: .

5. Plug in the values for the opposite side and the hypotenuse, but do not simplify to the final answer yet.

Try solving on your own before revealing the answer!

Q2. Convert the angle (given in degrees, minutes, and seconds) to a decimal in degrees. Round your answer to two decimal places.

Background

Topic: Angle Measurement Conversion

This question tests your ability to convert an angle from degrees, minutes, and seconds (DMS) to decimal degrees.

Key Terms and Formulas:

• Degrees (°), Minutes ('), Seconds (")

• Conversion: ,

• Decimal degrees = degrees + (minutes/60) + (seconds/3600)

Step-by-Step Guidance

1. Identify the number of degrees, minutes, and seconds in the given angle.

2. Convert the minutes to degrees by dividing by 60.

3. Convert the seconds to degrees by dividing by 3600.

4. Add all three values together to get the decimal degree measure.

5. Set up the calculation, but do not compute the final decimal value yet.

Try solving on your own before revealing the answer!

Q3. Convert the angle (given in decimal degrees) to degrees, minutes, and seconds (DMS) form. Round your answer to the nearest second.

Background

Topic: Angle Measurement Conversion

This question tests your ability to convert a decimal degree value into degrees, minutes, and seconds.

Key Terms and Formulas:

• Degrees (°), Minutes ('), Seconds (")

• To convert:

  • The whole number part is degrees.

  • Multiply the decimal part by 60 to get minutes.

  • Multiply the remaining decimal by 60 to get seconds.

Step-by-Step Guidance

1. Identify the whole number part of the decimal degree (this is the degrees).

2. Multiply the decimal part by 60 to get the minutes.

3. Take the decimal part of the minutes and multiply by 60 to get the seconds.

4. Round the seconds to the nearest whole number.

5. Set up the conversion, but do not write the final DMS value yet.

Try solving on your own before revealing the answer!

Q4. Convert the angle (given in degrees) to radians.

Background

Topic: Angle Measurement Conversion

This question tests your ability to convert an angle from degrees to radians.

Key Terms and Formulas:

• Degrees (°), Radians (rad)

• Conversion: radians

• Formula:

Step-by-Step Guidance

1. Write down the given angle in degrees.

2. Multiply the degree measure by to set up the conversion to radians.

3. Simplify the fraction if possible, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q5. Convert the angle (given in radians) to degrees.

Background

Topic: Angle Measurement Conversion

This question tests your ability to convert an angle from radians to degrees.

Key Terms and Formulas:

• Radians (rad), Degrees (°)

• Conversion:

• Formula:

Step-by-Step Guidance

1. Write down the given angle in radians.

2. Multiply the radian measure by to set up the conversion to degrees.

3. Simplify the expression if possible, but do not compute the final value yet.

Try solving on your own before revealing the answer!