Sage-Tips

What happens when a right triangle is rotated?

When a right angle triangle is rotated along its base, keeping the base horizontal, then other side of the right triangle is the vertica base height, and the hypotenuse is the slant height of the right circular cone.

What shape is obtained on rotating a right angled triangle about its shortest side?

Cone
A Cone is a Rotated Triangle A cone can be made by rotating a triangle! The triangle is a right-angled triangle, and it gets rotated around one of its two short sides. The side it rotates around is the axis of the cone.

What does an altitude do in a right triangle?

The altitude of a triangle is the perpendicular line segment drawn from the vertex of the triangle to the side opposite to it. The altitude makes a right angle with the base of the triangle that it touches. It is commonly referred to as the height of a triangle and is denoted by the letter ‘h’.

For which type of triangle is an altitude a side of the triangle?

isosceles triangle
In an isosceles triangle (a triangle with two congruent sides), the altitude having the incongruent side as its base will have the midpoint of that side as its foot. Also the altitude having the incongruent side as its base will be the angle bisector of the vertex angle.

What will be generated shape if a right angle triangle is rotated about one of its perpendicular sides?

Answer: When a right angled triangle is rotated on one of the side which is perpendicular to the base i.e. when a right angled triangle is rotated on the height of the triangle then a cone is formed such that it has following properties: The height of cone is same as height of the right angled triangle.

What is the altitude theorem?

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of the two segments equals the altitude.

Is each leg of a right triangle an altitude?

In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

Which triangle has its altitude in the exterior?

Obtuse angled triangle has altitude in exterior region of it But From the given options Scalene triangle can be the answer as only scalene triangle can be obtuse triangle in the given option.

What is the altitude of a right-angled triangle?

The altitude of a right-angled triangle divides the existing triangle into two similar triangles. According to right triangle altitude theorem , the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on hypotenuse.

What is the relationship between altitude and hypotenuse of a triangle?

This theorem describes the relationship between altitude drawn on the hypotenuse from vertex of the right angle and the segments into which hypotenuse is divided by altitude. Consider a right angled triangle, ∆ABC which is right angled at C. ii) Corresponding sides of both the triangles are in proportion to each other.

How to prove a triangle is a right angled triangle?

Thus, in a right angle triangle the altitude on hypotenuse is equal to the geometric mean of line segments formed by altitude on hypotenuse. The converse of above theorem is also true which states that any triangle is a right angled triangle, if altitude is equal to the geometric mean of line segments formed by the altitude.

What is the use of altitude in trigonometry?

The main use of the altitude is that it is used for area calculation of the triangle i.e. area of a triangle is (½ base × height). Now, using the area of a triangle and its height, the base can be easily calculated as Base = [ (2 × Area)/Height]