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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Angle measurement (degrees, radians)

Grade: 1400-a Lesson: S3-L6

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id	Problem	Options
1	Given a right triangle, where one of the acute angles measures 0.6 radians, determine the measurement of the other acute angle in both degrees and radians.	A) 61.22 degrees, 0.83 radians B) 55.6225 degrees, 0.97 radians C) 47.562 degrees, 0.5 radians D) 90 degrees, 3 radians
2	A wind turbine rotates at a speed of 60 revolutions per minute. How many radians does it turn in 2 minutes and 10 seconds?	A) 620π radians B) 260π radians C) 180π radians D) 300π radians
3	Astronomers are calibrating a new telescope to observe celestial objects. Initially, they must point the telescope at an angle of 30 degrees to focus on a star in the southern sky. Later, for a star in the northern sky, the telescope needs to be adjusted to 315 degrees. Convert these angles to radians for the telescope’s control system.	A) \$((2π)/6 , (3π)/4)\$ radians B) \$(π/2 , (3π)/7)\$ radians C) \$(π/6 , (2π)/7)\$ radians D) \$(π/6 , (7π)/4)\$ radians
4	A carpenter is constructing a circular table with a radius of 30 centimeters. They need to determine the angle subtended by an arc of 25 centimeters on the circumference of the table. To ensure accuracy in the design, they want this angle both in degrees and radians.	A) \$ 32^\circ \$ B) \$ 26.78^\circ \$ C) \$ 19.41^\circ\$ D) \$ 48.19^\circ\$
5	A circular flower bed has a radius of 3 meters. Gardeners want to place a decorative fountain in a sector formed by an arc with a central angle. If they want the arc length to be 4.5 meters, what is the degree measure of the central angle formed by this arc?	A) 35.6 degrees B) 40 degrees C) 42.8 degrees D) 59.6 degrees
6	A ladder 10 meters long leans against a vertical wall.The bottom of the ladder is 3 meters from the wall.What is the measure of the angle between the ladder and the ground,expressed in both degrees and radians?	A) 65.54 degrees, 1.27 radians B) 52.54 degrees, 1.16 radians C) 72.54 degrees, 1.26 radians D) 83.54 degrees, 1.56 radians
7	At what time between 3 o’clock and 4 o’clock will the minute and hour hands of a clock make an angle closest to 60°? Calculate the time to the nearest second.	A) 3:27 B) 4:17 C) 3:50 D) 4:48
8	The area of a sector is \$ 1225 "mm"^2 \$. If the radius of the sector is 36 mm, find the central angle of the sector in radians.	A) 1.889 B) 1.987 C) 1.932 D) 1.832
9	If \$"sin"("x") = 2/3 \$ and \$"cos"("y") = 3/5 \$, find the value of \$"sin"("x" + "y" ) \$ in radians.	A) \$ (3 + 2sqrt5)/15 \$ B) \$ (6 + 4sqrt5)/15 \$ C) \$ (3 + 4sqrt5)/10 \$ D) \$ (6 + 2sqrt5)/10 \$
10	A spotlight at the top of a buliding illuminates an area on the ground.If the angle of elevation of the spotlight is \$ (pi)/6 \$ radians and the buliding is 30 meters tall, find the diameter of the iilluminated circle on the ground.	A) \$ 40sqrt3 \$ meters B) \$ 60sqrt3 \$ meters C) \$ 60sqrt2 \$ meters D) \$ 40sqrt2 \$ meters

Problem Id

Problem

Options

Given a right triangle, where one of the acute angles measures 0.6 radians, determine the measurement of the other acute angle in both degrees and radians.

A) 61.22 degrees, 0.83 radians

B) 55.6225 degrees, 0.97 radians

C) 47.562 degrees, 0.5 radians

D) 90 degrees, 3 radians

A wind turbine rotates at a speed of 60 revolutions per minute. How many radians does it turn in 2 minutes and 10 seconds?

A) 620π radians

B) 260π radians

C) 180π radians

D) 300π radians

Astronomers are calibrating a new telescope to observe celestial objects. Initially, they must point the telescope at an angle of 30 degrees to focus on a star in the southern sky. Later, for a star in the northern sky, the telescope needs to be adjusted to 315 degrees. Convert these angles to radians for the telescope’s control system.

A) \$((2π)/6 , (3π)/4)\$ radians

B) \$(π/2 , (3π)/7)\$ radians

C) \$(π/6 , (2π)/7)\$ radians

D) \$(π/6 , (7π)/4)\$ radians

A carpenter is constructing a circular table with a radius of 30 centimeters. They need to determine the angle subtended by an arc of 25 centimeters on the circumference of the table. To ensure accuracy in the design, they want this angle both in degrees and radians.

A) \$ 32^\circ \$

B) \$ 26.78^\circ \$

C) \$ 19.41^\circ\$

D) \$ 48.19^\circ\$

A circular flower bed has a radius of 3 meters. Gardeners want to place a decorative fountain in a sector formed by an arc with a central angle. If they want the arc length to be 4.5 meters, what is the degree measure of the central angle formed by this arc?

A) 35.6 degrees

B) 40 degrees

C) 42.8 degrees

D) 59.6 degrees

A ladder 10 meters long leans against a vertical wall.The bottom of the ladder is 3 meters from the wall.What is the measure of the angle between the ladder and the ground,expressed in both degrees and radians?

A) 65.54 degrees, 1.27 radians

B) 52.54 degrees, 1.16 radians

C) 72.54 degrees, 1.26 radians

D) 83.54 degrees, 1.56 radians

At what time between 3 o’clock and 4 o’clock will the minute and hour hands of a clock make an angle closest to 60°? Calculate the time to the nearest second.

A) 3:27

B) 4:17

C) 3:50

D) 4:48

The area of a sector is \$ 1225 "mm"^2 \$. If the radius of the sector is 36 mm, find the central angle of the sector in radians.

A) 1.889

B) 1.987

C) 1.932

D) 1.832

If \$"sin"("x") = 2/3 \$ and \$"cos"("y") = 3/5 \$, find the value of \$"sin"("x" + "y" ) \$ in radians.

A) \$ (3 + 2sqrt5)/15 \$

B) \$ (6 + 4sqrt5)/15 \$

C) \$ (3 + 4sqrt5)/10 \$

D) \$ (6 + 2sqrt5)/10 \$

A spotlight at the top of a buliding illuminates an area on the ground.If the angle of elevation of the spotlight is \$ (pi)/6 \$ radians and the buliding is 30 meters tall, find the diameter of the iilluminated circle on the ground.

A) \$ 40sqrt3 \$ meters

B) \$ 60sqrt3 \$ meters

C) \$ 60sqrt2 \$ meters

D) \$ 40sqrt2 \$ meters