Question

3 What is the length of the missing leg? 15 m I meters

Answer 1

We'd use the pythagorean theorem to solve for the other leg's length. As the image suggests, we'd use the theorem,

`{a}^(2) + {b}^(2) = {c}^(2)`

If one leg is 9 , that's our a value.

If the hypotenuse is 15 , that's our c value.

Now we just have to find the b value.

Plugging in the variables,

`{9}^(2) + {b}^(2) = {15}^(2)`

`{9}^(2) = 81 \\ {15}^(2) = 225 \\ 81 + {b}^(2) = 225`

Subtract 81 from both sides.

`{b}^(2) = 144`

Square root both sides.

`\sqrt{ {b}^(2) } = b \: and \: √(144 = 12 )`

so b = 12

Answer 2

The length of the missing leg = 12 m

Step-by-step explanation

The triangle presented is a right angled triangle because one of its angles is equal to 90 degrees.

The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.

The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.

The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,

a² + b² = (hyp)²

For this question,

Hypotenuse side = 15 m

a = 9 m

b = d = ?

a² + b² = (hyp)²

9² + d² = (15)²

81 + d² = 225

d² = 225 - 81

d² = 144

d = √144

d = 12 m

Hope this Helps!!!