Pythagoras and Trigonometry

Question 1

What is the formula for Pythagoras’ theorem?

Answer 1

a^2 + b^2 = c^2 in any right angled triangle

Question 2

What is the length of c if a is 4 and b is 7

Answer 2

4 squared + 7 squared is 65
the square root of 65 is 8.06
8.06

Question 3

How do you find out if a triangle has a right angle or not?

Answer 3

If you know all three sides, you can apply Pythagoras theorem and see if it works out or not.

Question 4

Does this triangle contain a right angle?
a = 5
b = 12
c = 13

Answer 4

5* + 12* = c*
13* = 169
25+144 = 169

Yes the triangle does contain a right angle as Pythagoras theorem works out.

Question 5

How can you use Pythagoras to calculate the distance between to points on a graph

Answer 5

Join the points together and introduce them into the hypotenuse of a right angle triangle, you can then use Pythagoras theorem to find the distance.

Keep the measurements the same as on the axis

Question 6

How do you use Pythagoras theorem to find out the diagonal cross-section of a cube / cuboid?

Answer 6

1. Find the diagonal length of one long rectangle that will form the length needed for finding the diagonal cross-section
2. Use pythagoras theorem with the new-found length and the already known height being a and b

Question 7

Find the diagonal cross-section of the rectangle with width of 2cm, height of 3cm, and length of 6cm.

Answer 7

1. 2* + 6* = the length needed for the second triangle
   2* + 6* = 6.3
   6.3* + 3* = 49, the square root of 49 is 7
   A) 7