Question

How do you find the unknown length of a right triangle a=8, b=17 are the given side lengths?

Answer 1

Hint: The base and the height are often referred to as the legs of the right-angled triangle. The Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the squares of the base and the height. In this question, we are given the length of the base and the height of the right-angled triangle and we have to find the hypotenuse so using the Pythagoras theorem, we can find the relation between the three sides of the triangle and thus get an equation to find out the unknown quantity.

Complete step-by-step solution:
Let the length of the unknown side be “x”
Applying the Pythagoras theorem, we get –
$
  {(8)^2} + {(17)^2} = {x^2} \\
   \Rightarrow x = \sqrt {64 + 289} \\
   \Rightarrow x = \sqrt {353} \\
   \Rightarrow x = 18.79 \\
 $
Hence, the unknown length of the right triangle is $18.79$

Note: A triangle is defined as a polygon containing 3 sides and there are different types of triangles like a scalar triangle, equilateral triangle, isosceles triangle, right-angled triangle, etc. When any two sides of a triangle are perpendicular to each other, the triangle is defined as a right-angled triangle. The sides that are perpendicular to each other are known as the base and the height of the right-angled triangle and the line joining the other edge of both the sides is called the hypotenuse. In this triangle, one of the angles is of measure 90 degrees and length two sides of the triangle are given.