Question

14. Construction workers are laying out the rectangular foundation for a new building.They want to check that the corner is 90°. They measure the diagonal as shown to be 9.5 m. Is the angle 90° Explain your reasoning.

Answer 1

Step-by-step explanation: We can see on the image that the two sides and the diagonal represent a triangle. We also know that this triangle to have a 90 degrees angle is will be called a right triangle. Finally, all right triangles obey the Pythagorean equation

`h^2=a^2+b^2`

NOTE:

h = hypotenuse

a and b = other sides

Step 1: Once we know the length of the two sides we can use the Pythagorean equation to find the length of the hypotenuse for the triangle to be a right triangle and consequently have an angle that measures 90 degrees.

Step 2: Let's calculate as follows

`\begin{gathered} h^2=a^2+b^2 \\ h=\sqrt[]{8^2+6^2} \\ h=10 \end{gathered}`

Step 3: We can see above, that to have an angle that measures 90 degrees (right triangle) the triangle have to have a hypotenuse = 10 which is different from 9.5.

Final answer: So the angle does not measure 90°.