Triangle Height - Examples, Exercises and Solutions

In an isosceles triangle, the median to the base is also the height to the base.

That is, side AD forms a 90° angle with side BC.

That is, two right triangles are created.

Therefore, angle ADC is equal to 90 degrees.

The sum of angles in a triangle is 180 degrees. Since two angles of 90 degrees equal 180, a triangle can never have two right angles.

An altitude in a triangle is the segment that connects the vertex and the opposite side, in such a way that the segment forms a 90-degree angle with the side.

If we look at the image it is clear that the above theorem is true for the line AE. AE not only connects the A vertex with the opposite side. It also crosses BC forming a 90-degree angle. Undoubtedly making AE the altitude.

Every triangle has 3 sides, let's go over the triangle on the left side:

Its sides are: AB, BC, CA

This means that in this triangle, side EC does not exist.

Let's go over the triangle on the right side:

Its sides are: ED, EF, FD

This means that in this triangle, side EC does not exist.

Therefore, EC is not a side in either of the triangles.

Let's remember the definition of height of a triangle:

A height is a straight line that descends from the vertex of a triangle and forms a 90-degree angle with the opposite side.

The sides that form a 90-degree angle are sides AB and BC. Therefore, the height is AB.

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

Therefore, we will use the following formula:

$A+B+C=180$

Now let's input the known data:

$120+27+\alpha=180$

$147+\alpha=180$

We'll move the term to the other side and keep the appropriate sign:

$\alpha=180-147$

$\alpha=33$

Recall that the sum of angles in a triangle equals 180 degrees.

Therefore, we will use the following formula:

$A+B+C=180$

Now let's insert the known data:

$\alpha+50+50=180$

$\alpha+100=180$

We will simplify the expression and keep the appropriate sign:

$\alpha=180-100$

$\alpha=80$

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

Therefore, we will use the following formula:

$A+B+C=180$

Now let's input the known data:

$\alpha+69+23=180$

$\alpha+92=180$

We'll move the term to the other side and keep the appropriate sign:

$\alpha=180-92$

$\alpha=88$

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

Therefore, we will use the following formula:

$A+B+C=180$

Now let's input the known data:

$80+55+\alpha=180$

$135+\alpha=180$

We'll move the term to the other side and keep the appropriate sign:

$\alpha=180-135$

$\alpha=45$

It is known that the sum of angles in a triangle is 180 degrees.

Since we are given two angles, we can calculate $a$

$94+92=186$

We should note that the sum of the two given angles is greater than 180 degrees.

Therefore, there is no solution possible.

Let's remember that the sum of angles in a triangle is equal to 180.

Therefore, we will use the formula:

$A+B+C=180$

Let's input the known data:

$100+\alpha+90=180$

$190+\alpha=180$

$\alpha=180-190$

We should note that it's not possible to get a negative result, and therefore there is no solution.

First let's remember that the sum of the angles in a triangle is equal to 180 degrees.

Therefore, we can use the formula:

$A+B+C=180$

Then we will substitute in the known data:

$\alpha+27.7+41=180$

$\alpha+68.7=180$

Finally, we will move the variable to the other side while maintaining the appropriate sign:

$\alpha=180-68.7$

$\alpha=111.3$

Recall that the sum of angles in a triangle equals 180 degrees.

Let's add the three angles to see if their sum equals 180:

$60+50+70=180$

Therefore, it is possible that these are the values of angles in some triangle.

Let's calculate the sum of the angles to see what total we get in this triangle:

$56+89+17=162$

The sum of angles in a triangle is 180 degrees, so this sum is not possible.

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

We'll add the three angles to see if their sum equals 180:

$94+36.5+49.5=180$

Therefore, these could be the values of angles in some triangle.