Question

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

Answer 1

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

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

$\qquad \sf \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2}$

$\qquad \sf \dashrightarrow \: a {}^{2} = {15}^{2} - {9}^{2}$

$\qquad \sf \dashrightarrow \: a= \sqrt{225-81}$

$\qquad \sf \dashrightarrow \: a= \sqrt{144}$

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

Answer 2

Answer:

a = 12

Step-by-step 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