Trigonometry With General Triangles Assessment Test

The hypotenuse is the longest side of a right angle triangle. It is the side opposite the right angle and is always the longest side in a right triangle.

When the 3rd angle of an isosceles triangle is a right angle, it is called a right isosceles triangle because it has two equal sides and one right angle. In a right isosceles triangle, the two equal sides are the legs, and the right angle is formed by the intersection of the legs. This type of triangle is special because it combines the properties of both a right triangle and an isosceles triangle.

The Pythagorean theorem can be used to test whether a triangle has a right angle. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. By applying this theorem, one can determine if a triangle has a right angle by checking if the lengths of the sides satisfy this relationship.

The correct answer is 1/2bh. The formula for finding the area of a triangle is 1/2 times the base (b) times the height (h). This formula is derived from the fact that a triangle can be divided into two equal right triangles, and the area of a right triangle is 1/2 times the base times the height. Therefore, to find the area of any triangle, we can use the formula 1/2bh.

In an isosceles triangle, two sides are equal in length, while the third side, which is different in length, is called the base. Therefore, the correct answer is "Base".

The Law of Cosines is a mathematical formula that can be used to find missing angles in a triangle. It relates the lengths of the sides of a triangle to the cosine of one of its angles. By knowing the lengths of two sides and the included angle, or the lengths of all three sides, the Law of Cosines can be used to calculate the missing angles. This makes it a useful tool for solving triangle problems involving missing angles.

When two sides and an angle opposite one of them are known, it is called the ambiguous case. This means that there can be more than one possible solution for the triangle. In this case, additional information is needed to determine a unique triangle.

The perpendicular distance from the base of an isosceles triangle to the topmost vertex is called the altitude.

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side. This is a fundamental postulate in geometry that helps determine if a given set of side lengths can form a valid triangle. It is used to ensure that the triangle's sides do not overlap or form a straight line, which would not create a triangle. Therefore, the correct answer is Triangle Inequality Theorem.

The cosine rule can be used to find the length of a side or the size of an angle in a triangle. It relates the lengths of the sides of a triangle to the cosine of one of its angles. By rearranging the formula, we can solve for the length of a side or the size of an angle when the other values are known. This rule is particularly useful when dealing with non-right angled triangles.