When talking about the two hands of a clock, we refer to the hour hand and the minute hand. At 3:15, the hour hand points to 3 while the minute hand points to 15 on the clock face.
To determine the angle between the two hands, we need to first find the individual angles each hand makes with the 12 o’clock mark. The hour hand moves 30 degrees for every hour, which means it moves 90 degrees from the 12 o’clock mark to the 3 o’clock mark. Since it is halfway between the 3 o’clock and 4 o’clock marks, the hour hand has moved an additional 7.5 degrees.
Therefore, the angle the hour hand makes with the 12 o’clock mark is 90 + 7.5 = 97.5 degrees.
The minute hand, on the other hand, moves a full circle (360 degrees) in 60 minutes. This means it moves 6 degrees per minute. At 15 minutes past the hour, the minute hand has moved 6 x 15 = 90 degrees from the 12 o’clock mark, stopping at the 3 o’clock mark. Therefore, the angle the minute hand makes with the 12 o’clock mark is 90 degrees.
Now that we know the angles each hand makes with the 12 o’clock mark, we can determine the angle between the two hands. The minute hand is ahead of the hour hand by 97.5 – 90 = 7.5 degrees. Therefore, the angle between the two hands is 7.5 degrees.
The angle between the hour hand and minute hand of a clock at 3:15 is 7.5 degrees.
What angle the hands of a clock are inclined at 15 min past 3?
To answer this question, we must first understand the basic principles of a clock and how it displays time. Clocks are circular instruments that measure the passage of time using rotating hands. The standard clock has two hands, the hour hand and the minute hand, which rotate around a central point called the clock face.
The hour hand is typically shorter and thicker than the minute hand and shows the hour of the day while the minute hand shows the minutes.
When the time is at quarter past three, the hour hand is pointing towards the number three on the clock face, while the minute hand is pointing directly at the number 3. The angle between the two hands is calculated by subtracting the position of the hour hand from the position of the minute hand.
We can determine the position of the minute hand by using basic time unit conversion. At fifteen minutes past three, this means that the minute hand will be pointing directly at the number 3. On a clock face, the number 3 is located at a position of 90 degrees. Therefore, the position of the minute hand can be calculated to be 90 degrees.
Now, to determine the position of the hour hand, we must understand how it moves from hour to hour. A full rotation around the clock face by the hour hand takes 12 hours or 360°, and in one hour, the hand moves by 30°. In fifteen minutes, the hand moves by 1/4th of 30 degrees, that is 7.5°.
So, at fifteen minutes past three, the hour hand will have moved 7.5 ° from its previous position. Since its previous position was on the number three, adding 7.5° to the 90° position of the minute hand gives us a total angle of 97.5° between the two hands at fifteen minutes past three.
To summarize, the angle between the hands of a clock at fifteen minutes past three is 97.5 degrees.
What is the formula for angle in clock?
The formula for the angle in a clock can be determined by using simple mathematics. A clock is a circle, with 360 degrees in total. Since there are 12 numbers on the clock face representing the hours in a day, each number is separated by 30 degrees (360 divided by 12 equals 30).
To find the angle made by the hour hand, the formula is:
Angle made by hour hand = (30 x hours) + (0.5 x minutes)
For example, if the time is 4:45, the angle made by the hour hand can be calculated as:
(30 x 4) + (0.5 x 45) = 120 + 22.5 = 142.5 degrees
The formula for the angle made by the minute hand is simpler:
Angle made by minute hand = (6 x minutes)
For example, if the time is 4:45, the angle made by the minute hand can be calculated as:
6 x 45 = 270 degrees
The formulas to find the angle made by the hour hand and minute hand on a clock are quite simple. Knowing these formulas, we can quickly and accurately calculate the angles made by the hands at any given time.
How many degrees is 5pm between the clock hands?
To answer this question, we need to understand how to calculate the angle between the hour and minute hands on a clock.
The hour hand moves 30 degrees for every hour, and the minute hand moves 6 degrees for every minute.
So, at 5:00 pm, the hour hand has moved 5 hours from the 12 o’clock position. Therefore, the angle of the hour hand from the 12 o’clock position is 5 x 30 = 150 degrees.
The minute hand is pointing directly at the 12 o’clock position because it is exactly on the hour. Therefore, the angle of the minute hand from the 12 o’clock position is 0 degrees.
To find the angle between the two clock hands, we need to find the difference between the angles of the hour and minute hands.
In this case, the angle between the hands is 150 – 0 = 150 degrees. So, the angle between the clock hands at 5:00 pm is 150 degrees.
What are 2 45 degree angles?
Two 45 degree angles are two angles that measure 45 degrees each. A degree is a unit of measurement for angles, and it is denoted by the symbol “°”. An angle is formed when two lines or rays meet at a point, and the amount of turn from one line or ray to the other is measured in degrees.
In the case of two 45 degree angles, each angle measures exactly 45 degrees. This means that if we were to take a protractor and measure the angle between the two lines or rays that form each of these angles, we would get a reading of 45 degrees. To give an example, we can draw two intersecting lines and mark a point of intersection.
By placing the protractor with its base on the intersection point and its zero line aligned with one of the lines, we can measure an angle of 45 degrees between that line and the other line. Similarly, if we measure the angle between the second line and the first line using the protractor, we would get another reading of 45 degrees.
It’s important to note that two 45 degree angles are also known as congruent angles. Congruent angles are angles that have the same measure, meaning they are identical in size and shape. Therefore, if we have two 45 degree angles, we can say that they are congruent to each other because they have the same measure of 45 degrees.
Two 45 degree angles refer to two angles that measure exactly 45 degrees each. They are formed when two lines or rays meet at a point and turn 45 degrees between each other. These angles are also known as congruent angles because they have identical size and shape, and they are denoted by the symbol “∠45°.”
What angle is a 35% slope?
A 35% slope angle can be determined using trigonometry. First, we need to convert the percentage to a decimal value. To do this, we divide the percentage by 100. Therefore, 35% is equivalent to 0.35.
Now, let’s assume that we have a right triangle where the slope is the hypotenuse and the base is the horizontal distance. The angle we are looking for is opposite to the height, which represents the vertical distance.
To find the angle, we can use the inverse tangent function (tan inverse) which is defined as the ratio of the height to the base. This can be represented mathematically as:
tan(angle) = height / base
Therefore, angle = tan inverse (height / base)
Let’s say that the height of the slope is 10 units and the base is 20 units. We can plug in these values into the equation and solve for the angle as:
angle = tan inverse (10 / 20)
angle = tan inverse (0.5)
Using a calculator, we can evaluate the inverse tangent of 0.5, which is approximately 26.6 degrees.
So, the angle of a 35% slope is approximately 26.6 degrees. This means that for every 100 units traveled horizontally, the slope rises 35 units vertically and the angle of inclination is 26.6 degrees from the horizontal.
