Question

Please I need help only 1-4
Pythagorean theorem

Answer 1

Question 1

This is a special triangle as the angles are 30-60-90

This means that the sides have a special ratio of
1 : √3 : 2 = short leg : long leg : hypotenuse

So the hypotenuse is twice the length of the short leg,
and the long leg is √3 times the length of the short leg.

Given:

• short leg = x
• long leg = y
• hypotenuse = 30

⇒ x = 30 ÷ 2 = 15

⇒ y = 15 × √3 = 15√3

Question 2

The sum of the interior angles of a triangle is 180°. Therefore the unknown angle of the triangle is 60°.

So again, this is a special 30-60-90 triangle, and we can use the same method as question 1 above.

Given:

• short leg = 5
• long leg = x
• hypotenuse = y

⇒ x = 5 × √3 = 5√3

⇒ y = 5 × 2 = 10

Question 3

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

To find x:

Given:

• a = 8
• b = 6
• c = x

⇒ 8² + 6² = x²

⇒ x² = 100

⇒ x = √100

⇒ x = 10

To find y:

Given:

• a = 5
• b = x = 10
• c = y

⇒ 5² + 10² = y²

⇒ y² = 125

⇒ y = √125

⇒ y = 5√5

Question 4

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

To find x:

Given:

• a = 5
• b = 12
• c = x

⇒ 5² + 12² = x²

⇒ x² = 169

⇒ x = √169

⇒ x = 13

To find y:

Given:

• a = y
• b = x = 13
• c = 14

⇒ y² + 13² = 14²

⇒ y² + 169 = 196

⇒ y² = 27

⇒ y = √27

⇒ y = 3√3