Understanding Related Rates in Triangles

This tutorial focuses on solving related rate problems involving triangles. It begins with a right triangle where the base and height are increasing at known rates, and the task is to find how fast the area is changing. The solution involves using differentiation and the product rule. The tutorial then moves to a generic triangle with fixed side lengths and an increasing angle, using the sine rule to find the rate of area change. The video concludes with a summary of the methods used to solve these problems.

What is the rate at which the base of the right triangle is increasing?

• 4 cm/min

• 3 cm/min

• 2 cm/min

• 5 cm/min

Which mathematical rule is used to differentiate the area of the right triangle with respect to time?

• Quotient Rule

• Chain Rule

• Product Rule

• Power Rule

What is the rate of change of the area of the right triangle when the base is 8 cm and the height is 10 cm?

• 40 square cm/min

• 35 square cm/min

• 30 square cm/min

• 25 square cm/min

In the generic triangle problem, what are the fixed lengths of the two sides?

• 3 meters and 6 meters

• 4 meters and 7 meters

• 5 meters and 8 meters

• 6 meters and 9 meters

What is the formula for the area of a triangle with two sides and an included angle?

• a * b * cos(C)

• 1/2 * a * b * sin(C)

• a * b * sin(C)

• 1/2 * a * b * cos(C)

What is the rate at which the angle between the two sides of the generic triangle is increasing?

• 0.10 radians/min

• 0.20 radians/min

• 0.25 radians/min

• 0.15 radians/min

Why are the rates of change for sides a and b not considered in the generic triangle problem?

• They are variables.

• They are constants.

• They are irrelevant.

• They are not given.

What is the derivative of sine in the context of differentiating the area of the generic triangle?

• Tangent

• Secant

• Cosine

• Sine

What is the unit of the rate of change of the area of the generic triangle?

• Square meters per minute

• Square meters per second

• Square centimeters per second

• Square centimeters per minute

How much does the area of the generic triangle increase in 10 minutes?

• 12 square meters

• 10 square meters

• 18 square meters

• 15 square meters