Find the value of x using special right triangles

Question

it is a right triangle and it is only given the 90 degree angle and the other two angles are not shown. Also the hypotenuse is 7 to the square root of 2. You have to solve for the other two sides which are shown as x

Answer 1

in a 45º-45º-90º isosceles right triangle, the hypotenuse is always equal to the length of a side times √2

if the length of each side is given as x, then the hypotenuse is x√2

if the hypotenuse is 7√2 and the other two sides are shown as x, then x=7 (both sides equal 7)

check: 7^2+7^2=(7√2)^2

          49+49=7^2*(√2)^2

          49+49=49*2

          98=98

Answer 2

Hi Rishika, if you have a right triangle with both legs equal to x, then you have a right-45 degree triangle. The missing angles are 45 degrees each.

 

For a right-45 degree triangle, use the ratios 1, 1, √2 to find the lengths of the legs and hypotenuse.

 

You are given the length of the hypotenuse as 7√2. 

 

Using ratio:

 

Let x represent the length of one of the legs.

 

x / 1 = 7√2 / √2

 

x = 7

 

The two legs of the triangle are 7 units.

 

Questions?