How to find the heights of a triangle

Geometry is not only a school subject for which you need to get a good grade. The calculation of the height of the triangle may be needed in practical life. For example, if you are building a house with a high roof and you need to calculate the number and thickness of logs.

You will need

Ruler Angle Pencil Protractor Tables of sines and cosines

Instruction manual

one

Build a triangle with the given parameters. You know either the two angles of the triangle and the side between them, or the angle and length of the two sides between which it is located, or three sides.

Designate the vertices of the corners of the triangle as A, B and C. Designate the angles respectively as?, ?, ? Opposite sides, designate as a, b, c.

Remember what height is. This is a perpendicular drawn from the corner of the triangle to its opposite side. Take a square and draw such perpendiculars to all sides of the triangle. Denote the heights by the letter h with the corresponding sides of the triangle by the indices a, b, c.

2

Calculate the length of all sides of the triangle and all its angles using the theorems of sines and cosines.

Calculate the height omitted from the given angle using the formula: the height omitted from angle C is the product of the sine of any other angle and the length of the side adjacent to it.

note

The heights of an acute-angled triangle are inside it. An obtuse triangle has one height (the one that comes from an obtuse angle) that passes inside the triangle, and the other two outside it. In a right triangle, two heights coincide with the legs, and one is inside the triangle. All three heights intersect in the orthocenter, which can be inside, outside or on the leg of the triangle. In a right triangle, two heights are known, since they are legs. We find the third height by the Pythagorean theorem, taking the square of the AD segment from the square of the segment AC, which is simultaneously the hypotenuse of the triangle CDA. The size of this segment is easy to calculate, knowing the similarity of triangles. Hypotenuse AB refers to the hypotenuse of CB in the same way as the side of the BC refers to side of the DB. The sides of a right triangle are calculated by the Pythagorean theorem. The sides of an acute-angled triangle are calculated by the sine or cosine theorems

Useful advice

Use math tables to determine sines and cosines.