Exploring Problem Solving Techniques in Trigonometry

This video tutorial covers the use of trigonometric functions, specifically sine, to derive a new area formula for triangles when the height is not given. It includes example problems to apply the formula and explains how to solve right triangles using the Pythagorean theorem and trigonometric ratios. The tutorial also demonstrates solving triangles located on a coordinate plane, emphasizing the use of the distance formula and verifying right angles through slope calculations.

What is the new area formula derived for a triangle?

• Area = base * height

• Area = a * b * sin(C)

• Area = 1/2 * base * height

• Area = 1/2 * a * b * sin(C)

Does the derived area formula work if angle C is a right angle?

• Yes, it simplifies to 1/2 * a * b

• No, it only works for acute angles

• Yes, but it becomes 1/2 * a * b * cos(C)

• No, it requires an obtuse angle

How do you find the area of a triangle when given two sides and the included angle?

• Add the sides and multiply by the sine of the angle

• Substitute the values into the formula 1/2 * a * b * sin(C)

• Use the Pythagorean theorem

• Multiply the sides and divide by 2

What is required to solve a right triangle?

• One side length only

• Two angles and one side length

• Three side lengths

• Two side lengths or one side length and one acute angle

How do you find the length of a side in a right triangle using trigonometry?

• Multiplying the hypotenuse by the sine of the given angle

• Using the sine function only

• Applying the Pythagorean theorem

• Using any trigonometric ratio that fits the given information

What is the purpose of using inverse trigonometric functions in solving triangles?

• To find the measures of angles

• To determine if the triangle is right-angled

• To calculate the area of the triangle

• To find the length of sides

How can the distance formula be used in trigonometry on the coordinate plane?

• To calculate the area of any triangle

• To find the hypotenuse of a right triangle

• To determine the slope of a line

• To find the length of sides not on the axes

What verifies that a triangle on the coordinate plane is a right triangle?

• If it can be inscribed in a circle

• If the hypotenuse is the longest side

• If the slopes of two sides are opposite reciprocals

• If it has a 90-degree angle

What is the result of applying the inverse sine function to a ratio in solving a triangle?

• The length of the opposite side

• The area of the triangle

• The measure of an acute angle

• The length of the hypotenuse

In a 45-45-90 triangle, if one leg is 5 units, what is the length of the hypotenuse?

• 5 units

• 5√2 units

• 10 units

• 7.5 units