The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate sec. How fast is the top of the ladder moving up the wall 12 seconds after we start pushing? 5 at 12 sec, it is 10+ * 12 = 10-3=7 ft.

A 10-ft ladder is leaning against a house on flat ground. The house is to the left of the ladder. The base of the ladder starts to slide away from the house. When the base has slid to 8 ft from the house, it is moving horizontally at the rate of 2 ft/sec.

A “related rates” problem is a problem which involves at least two changing quantities and asks you to figure out the rate at which one is changing given sufficient information on all of the others. Solve for the quantity wanted. Go back over your work and write up a presentable solution.

The altitude of a triangle is increasing at a rate of 1.500 centimeters/minute while the area of the triangle is increasing at a rate of 3.000 square centimeters/minute.

Steps in Solving Time Rates Problem

1. Identify what are changing and what are fixed.
2. Assign variables to those that are changing and appropriate value (constant) to those that are fixed.
3. Create an equation relating all the variables and constants in Step 2.
4. Differentiate the equation with respect to time.

In each case you’re given the rate at which one quantity is changing. That is, you’re given the value of the derivative with respect to time of that quantity: When a quantity is decreasing, we have to make the rate negative.

Let’s use our Problem Solving Strategy to answer the question.

1. Draw a picture of the physical situation. See the figure.
2. Write an equation that relates the quantities of interest. A.
3. Take the derivative with respect to time of both sides of your equation. Remember the chain rule.
4. Solve for the quantity you’re after.

Formulas for right triangles If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side.

So the rate of change of the angle of elevation when the balloon is 18 feet high is approximately equal to 0.0485 radians per second.

tan θ = y/x; cot θ = x/y. depending upon the data given in the question, corresponding formula is applied to find out the angle of elevation. Here SR is the height of man as ‘l’ units and height of pole to be considered will be (h – l) units. The line of sight in this case will be PS and angle of elevation will be ‘θ’.

The reference angle must be <90∘. Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis.

Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.

60°

As per the definition of reflex angle, any degree which lies between straight angle (180°) and full rotation (360°) is a reflex angle. Hence, 181°, 190°, 200°, 210°, 220°, 230°, 240°, 250°, 260°, 270°, 280°, 290°, 300°, 310°, 320°, 330°, 340°, 350°, 359°, are all reflex angles.

50°

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 360° if the angle is measured in degrees or 2π if the angle is measured in radians . Example 1: Find a positive and a negative angle coterminal with a 55° angle.

In Mathematics, the coterminal angle is defined as an angle, where two angles are drawn in the standard position. Also both have their terminal sides in the same location. For example, the coterminal angle of 45 is 405 and -315.

Coterminal angle of 120° (2π / 3): 480°, 840°, -240°, -600° Coterminal angle of 135° (3π / 4): 495°, 855°, -225°, -585°

An angle measuring 70 degrees is coterminal with an angle measuring 430 degrees. The angle measuring 430 degrees is actually 360 + 70 (one full revolution plus the original 70). This pattern could go on and on, with the addition of another 360 degrees each time.

A “related rates” problem is a problem which involves at least two changing quantities and asks you to figure out the rate at which one is changing given sufficient information on all of the others.

Rewrite the following formula with the numerical equivalents: Object Height / tan θ = Shadow Length. For example, for the 790-foot high Prudential Tower in Boston, the formula would be 790 / 2.89 = Shadow Length. Calculate the formula to determine the shadow length.

45°

Next we would calculate the reference angle. 210 degrees is 30 degrees past 180, which means the reference angle is 30 degrees.

Since the terminal side of the 150° is only thirty degrees from the (negative) x-axis (being thirty degrees less than 180°, which is the negative x-axis), then the reference angle (again shown by the curved purple line) is 30°. Continuing around counter-clockwise, we can graph 210°. So its reference angle is 30°.

Terms in this set (7)

• sin210. -1/2.
• cos210. -√3/2.
• tan210. √3/3.
• cot210. √3.
• sec210. -2√3/3.
• csc210. -2.
• radian name. 7π/6.

π2 radians

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

This means that its complement is 90 – x degrees. But the difference in their measures is 12 degrees.