Question

in the right triangle above, ( a = 9.9 ) and ( c = 12.4 ). find the value of ( b ), rounded to the nearest tenth.
a 2.5
b. 4.7
c. 7.5
d. 22.3
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, so rearrange to solve for $b$:
$b = \sqrt{c^2 - a^2}$

Step2: Substitute given values

Substitute $a=9.9$, $c=12.4$:
$b = \sqrt{(12.4)^2 - (9.9)^2}$

Step3: Calculate squared terms

Compute the squares:
$(12.4)^2 = 153.76$, $(9.9)^2 = 98.01$

Step4: Subtract and take square root

Find the difference and square root:
$b = \sqrt{153.76 - 98.01} = \sqrt{55.75} \approx 7.5$

Answer:

C. 7.5