Arc Length
Write down two different versions of the arc length equation
L = 2*pi*r*angle/360 or L = theta*r
Write down two different versions of the area of sector equation
A = pi*r^2*angle/360 or A = (1/2)*theta*r^2
What are the equations for angular velocity and linear velocity?
Angular velocity = w = theta/t
Linear velocity = wr = theta/t*r
Use either the Law of Sines or Law of Cosines to find the remaining side c:
a= 10, b = 10, angle C = 60 degrees
c = 10 (it's an equilateral triangle!)
Why can we not use the Law of Sines on a triangle that has only two sides given and only the angle in between them given?
Law of Sines requires an known angle and a corresponding known side length to use the proportions to solve for another part of the triangle
Find the length of an arc that subtends [forms] a central angle of 45° in a circle of radius 10 m.
7.85 m
Find the area of a sector of a circle that has a radius of 18 cm and an angle of 60 degrees.
169.6 square centimeters
A radial saw has a blade with a 6-in radius. Suppose the blade spins at 1000 rpm. Find the angular velocity (in radians per second) and linear velocity (in feet per second) of the tip of the blade
104.7 rad/sec and 52.4 ft/sec
How many possible triangles are there for the following information?
angle A = 100, a = 33, b = 29
No triangles possible
When we have a triangle with two given angles and a side that is in between those angles, can we use the Law of Sines? Why or why not?
Yes we can use the Law of Sines! We can find the third angle by subtracting the other two angles from 180 degrees.
An arc of length 100 m subtends [forms] a central angle in a circle of radius 50 m. Find the measure of the angle in radians and degrees.
angle = 2 radians or 114.6 degrees
A lawn sprinkler located at the corner of a yard is set to rotate through 90° and project water out 30 feet. What area of the lawn is watered by the sprinkler?
707 square feet
A wind machine used to generate electricity has blades that are 10 ft in length. The propeller is rotating at 4 revolutions per second. Find the linear speed of the tips of the blades in ft/min.
15080 ft/min
How many possible triangles are there for the following information?
angle A = 131, a = 25, b = 8
One triangle only (the other one's angles add up to more than 180 degrees)
(Picture will be drawn on the board)
Use Law of Cosines to find the first angle, then Law of Sines to find the second angle, then subtract the two angles you have from 180 degrees to find the last angle
or use law of cosines three times to find each angle!
Memphis, TN and New Orleans, LA lie approximately on the same meridian (longitude line). Memphis has a latitude 35°N and New Orleans has a latitude 30°N. Find the distance between these cities if the radius of the earth is 3960 mi.
345.6 mi
A windshield wiper wipes through angle of 120° and clears an area of 368 square inches. How long is the windshield wiper?
18.75 inches
The wheels of a car have a diameter of 22 in and are rotating at 600 rpm. Find the speed of the car in mi/hr.
39.3 mph
Two fire towers are located 10 miles apart from each other (east to west). The ranger from Tower A spots a fire 42 degrees north of the other tower. The ranger from Tower B spots the same fire 64 degrees north of the other tower. How far from Tower A is the fire?
9.35 miles
(Picture will be drawn on the board)
Use law of cosines on the triangle on the right to find the length of the vertical side in the center, then use law of sines on the triangle on the left to find desired angle