Question

How to calculate the hypotenuse of the right triangle with one length?

Answer 1

Hint: Here, we will use the fact that the given data includes the length of one side other than the hypotenuse and the measure of the right angle i.e. 90 degrees. Thus, we will find whether there is any method that exists in order to find the hypotenuse with the given information or the information is insufficient. Thus, this will give us the required answer.

Complete step-by-step answer:
In order to calculate hypotenuse of a triangle, we usually use the Pythagoras Theorem.
According to this theorem,
The sum of the square of two sides i.e. the base and the perpendicular side of any right angled triangle is equal to the square of the longest side, i.e. the hypotenuse.
Hence, this can be written as:
${\left( B \right)^2} + {\left( P \right)^2} = {\left( H \right)^2}$
Where, $B,P,H$ represent the base, perpendicular and the hypotenuse side respectively.
But, if we have only one length with us i.e. either the base or the perpendicular side and we are required to find the hypotenuse.
Then, in this formula, two sides will be missing and only one side is known by us. Thus, this couldn’t be solved further.
Also, we could have still solved for the hypotenuse if one angle and two sides containing that angle i.e. SAS or one side and two angles i.e. ASA or measure of all the three sides i.e. SSS is given to us.
But, in this question, we are having just one side and only a single angle i.e. the right angle. Thus, the information is insufficient and hence, this couldn’t be solved further.
Therefore, we cannot calculate the hypotenuse of any right triangle with only one length.
Hence, the given data is insufficient.

Note:
Right angled triangle is any triangle whose one angle is always 90 degrees or in other words a right angle. The side opposite the angle 90 degree is the hypotenuse or the longest side. In a right angled triangle, the hypotenuse is always the longest side. The other two sides adjacent to the right angle are called base and perpendicular. The sum of the other two interior angles is equal to 90 degrees because one angle is already 90 degrees and we know that the sum of interior angles of a triangle is 180 degrees.