Pythagorean theorem

Question

Determine the lengths of the unknown sides in the following triangles using the Pythagorean theorem:

 

1) Leg A= x
Leg B= 8
Hypotenuse= 10


2) Leg A= m
Leg B= 3.6
Hypotenuse= 6.0


3) Leg A= y
Leg B= y
Hypotenuse= 4


4) Leg A= 10
Leg B= 4
Hypotenuse= n

Answer 1

Amber,

 

The Pythagorean Theorem states that, in any right triangle with legs a, b, and hypotenuse c, a² + b² = c².

 

1) x² + 8² = 10²  ⇒  x² + 64 = 100  ⇒  x² = 36  ⇒  x = 8

 

2) m² + 3.6² = 6.0²  ⇒  m² + 12.96 = 36.00  ⇒ m² = 23.04  ⇒ x = √23.04 = 4.8

 

3) y² + y² = 4²  ⇒  2y² = 16  ⇒  y² = 8  ⇒  y = √8 = 2√2 ≈ 2.828

 

4) 10² + 4² = n²  ⇒  n² = 116  ⇒  n = √116 = 2√29 ≈ 10.770

 

I cannot answer the remaining questions because you did not provide the necessary information.