Use the Pythagorean Theorem to SHOW that a triangle with sid

Use the Pythagorean Theorem to SHOW that a triangle with sides Squareroot 34, 4, and 5 Squareroot 2 is a right triangle Find the measure of the angles in degrees for the triangle in 3a. Angle A = 67.0 degree Angle B = 23. degree Angle C = 90.0 degree

Solution

Use pythogorean theorem : c^2 = a^2 + b^2

take the largest side as c = 5sqrt(2)

So, (5sqrt2)^2 = ( sqrt34)^2 + 4^2

50 = 34 + 16

50 = 50

This obeys pythogorean theoerm .Hence given triangle is a right angled triangle

Now to find the measure of angles : c as hypotenuse , a as height and b as base of triangle

cosA = 4/5sqrt(2) = 0.565

A = 55.55 deg

B = 180 - 90 - 55.55 = 34.44 deg