Question

Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. The diagram is not drawn to scale.

Answer 1

You've got a right triangle here with one leg = 7, and one angle = 45 degrees. That means the other angle must also be 45 degrees (sum of the interior angles of a triangle = 180, so 180-90-45 = 45). With equal angles, the two sides opposite the hypotenuse must be equal. Finally, you can find the length of the hypotenuse with the Pythgorean theorem, \[a^2+b^2=c^2\] where \(a,b\) are the legs of the triangle adjacent to the right angle and \(c\) is the hypotenuse. You know that \(a = 7, b = 7\) by the geometry of the triangle, so square the numbers, add them, and find the square root to give you the length of the remaining side.

Answer 2

ok thank you