Question

Find the length of the missing leg

Answer 1

The length of the missing leg is 12 m.

Step-by-step explanation:

SOLUTION :

Here we have given that the base of triangle is 9 m and hypotenuse is 15 m. We have to find the the height of triangle.

Using Pythagoras Theorem to find the height of triangle :

`\quad{\longrightarrow{\sf{{(H)}^(2) = {(b)}^(2) + {(h)}^(2)}}}`

• H = hypotenuse
• b = base
• h = height

Substituting all the given values in the formula to find the height of triangle :

`\quad{\longrightarrow{\sf{{(H)}^(2) = {(b)}^(2) + {(h)}^(2)}}}`

• b = 9 m
• H = 15 m

`\quad{\longrightarrow{\sf{{(15)}^(2) = {(9)}^(2) + {(h)}^(2)}}}`

`\quad{\longrightarrow{\sf{{(15 * 15)} = {(9 * 9)} + {(h)}^(2)}}}`

`\quad{\longrightarrow{\sf{{(225)} = {(81)} + {(h)}^(2)}}}`

`\quad{\longrightarrow{\sf{{(h)}^(2) = 225 - 81}}}`

`\quad{\longrightarrow{\sf{{(h)}^(2) = 144}}}`

`\quad{\longrightarrow{\sf{h = √(144)}}}`

`\quad{\longrightarrow{\sf{\underline{\underline{\pink{h = 12 \: m}}}}}}`

Hence, the height of triangle is 12 m.

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Answer 2

12 m

Explanation:

Since this is a right triangle, let's use the Pythagorean Theorem.

Recall that the Pythagorean Theorem is:

`a^2+b^2=c^2`

Where a is the length of one of the legs, b is the length of the other leg, and c is the length of the hypotenuse.

We are given the hypotenuse (15 m) and one of the legs (9 m).

Let's assign some values:

`a=??\\c=15\\b=9`

Let's solve for b by using the Pythagorean Theorem.

`a^2+b^2=c^2=\\a^2+9^2=15^2=\\a^2+81=225=\\a^2=144=\\a=12`

So, the length of the missing leg, a, is 12 m.