Question

for the triangle shown, which expression represents the value of ( a )?
( \bigcirc quad sqrt{21^2 - 6^2} )
( \bigcirc quad 21^2 - 6^2 )
( \bigcirc quad sqrt{21 - 6} )
( \bigcirc quad 21 - 6 )
note: figure not drawn to scale.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \( c^2 = a^2 + b^2 \), where \( c \) is hypotenuse, \( a,b \) are legs. Here, hypotenuse \( c = 21 \), one leg \( b = 6 \), find \( a \). Rearranging: \( a^2 = c^2 - b^2 \), so \( a=\sqrt{c^2 - b^2} \).

Step2: Substitute values

Substitute \( c = 21 \), \( b = 6 \): \( a=\sqrt{21^2 - 6^2} \).

Answer:

\(\sqrt{21^2 - 6^2}\) (the first option)