Triangle Area Calculation Using Sine Function

This video tutorial explains how to find the area of a triangle using the sine function, specifically when given two sides and the included angle (SAS). It covers the derivation of the formula, provides two example problems, and discusses the importance of the included angle. The tutorial also touches on the law of sines to solve for unknown angles, ensuring a comprehensive understanding of the topic.

What is the primary goal of using the sine function in this lesson?

• To find the hypotenuse of a right triangle

• To calculate the volume of a triangle

• To determine the area of a triangle given side-angle-side

• To find the perimeter of a triangle

Which angle is crucial when using the sine formulas to find the area of a triangle?

• Any angle

• The included angle

• The largest angle

• The smallest angle

What is the relationship between the sides and angles in a triangle?

• Side b is opposite angle c

• Side c is opposite angle a

• Side a is opposite angle b

• Side a is opposite angle a

How is the height of a triangle related to the sine of an angle in the derivation?

• Height is equal to base times sine of angle

• Height is equal to side times sine of angle

• Height is equal to sine of angle divided by side

• Height is equal to angle times sine of side

What is the area of a triangle with sides 6 cm and 15 cm, and an included angle of 63 degrees?

• 30 square centimeters

• 40 square centimeters

• 60 square centimeters

• 50 square centimeters

In the first example problem, what is the measure of angle C?

• 35 degrees

• 82 degrees

• 63 degrees

• 45 degrees

What is the first step in solving the second example problem?

• Find the length of side c

• Calculate the area directly

• Use the Pythagorean theorem

• Find the measure of angle a

What is the approximate area of the triangle in the second example problem?

• 587 square feet

• 487 square feet

• 387 square feet

• 287 square feet

Which law is used to find the missing angle in the second example problem?

• Law of Cosines

• Law of Tangents

• Law of Sines

• Law of Secants

Why is the angle of 140 degrees not possible in the second example problem?

• It is not a valid angle in any triangle

• It is not an included angle

• It exceeds the sum of 180 degrees with another angle

• It is less than 72 degrees