PreCalculus: 6.1 & 6.2

If two sides a and b and the included angle C are known in a​ triangle, then the area of the triangle is found using the formula ______________.

Area = 1/2ab • sinC

The area of a triangle equals one-half the product of the lengths of two sides times the sine of their included angle. This wording can be expressed by the formulas ___________________.

Area = 1/2bc • sinA Area = 1/2ab • sinC Area = 1/2ac • sinB

Heron's Formula

Area = √S(S - a)(S - b)(S - c), where S = 1/2(a + b + c)

To solve an oblique triangle given three sides​ (SSS), the first step is to find the angle opposite the longest side using the Law of _______. Then we find either of the two remaining acute angles using the Law _______.

Cosines, Sines

To solve an oblique triangle given two sides and an included angle​ (SAS), the first step is to find the missing side using the Law of __________. Then we use the Law of __________ to find the angle opposite the shorter of the two given sides. This angle is always __________. The third angle is found by subtracting the measure of the given angle and the angle found in the second step from ______ degrees.

Cosines, Sines, acute, 180

True or​ false: A triangle in which two sides and an angle opposite one of them are given​ (SSA) always results in at least one triangle.

The statement is false because an oblique triangle in which two sides and an angle are given results in an ambiguous case. The result may be one​ triangle, two​ triangles, or no triangle at all.

We can always use the Law of Sines to find missing parts of triangles in which one _________ and two _________ are known.

side, angles

You would generally use the Law of Cosines when given _______________.

three different letters (ex. a, b, & C)

There is no triangle when _______.

a < h

There is one triangle when _______.

a ≥ h and a < b

There are two triangles when _______.

a ≥ h and a > b

Law of Sines

a/sinA = b/sinB = c/sinC

Law of Cosines

a² = b² + c² - 2bc • Cos A b² = a² + c² - 2ac • Cos B c² = a² + b² - 2ab • Cos C

You use Heron's formula to find the area of a triangle when ___________.

each side length is different

A triangle that does not contain a right angle is called​ a/an ________.

oblique triangle