Question

Does someone mind helping me with this problem? Thank you!

Answer 1

a = 12

Explanation:

Pythagoras’ Theorem

a² + b² = c²

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

From inspection of the triangle:

• leg a = a
• leg b = 9
• hypotenuse c = 15

Substituting these values into the formula and solving for b:

⇒ a² + 9² = 15²

⇒ a² + 81 = 225

Subtract 81 from both sides:

⇒ a² + 81 - 81 = 225 - 81

⇒ a² = 144

Square root both sides:

⇒ √(a²) = √(144)

⇒ a = 12

Answer 2

`\qquad\qquad\huge\underline{{\sf Answer}}`

Let's calculate the value of a using Pythagoras theorem ~

`\qquad \sf  \dashrightarrow \: c {}^(2) = a {}^(2) + {b}^(2)`

`\qquad \sf  \dashrightarrow \: a {}^(2) = {15}^(2) - {9}^(2)`

`\qquad \sf  \dashrightarrow \: a= √(225-81)`

`\qquad \sf  \dashrightarrow \: a= √(144)`

`\qquad \sf  \dashrightarrow \: a= 12\: units`