Question

finding a missing side using the pythagorean theorem
find the missing sides of the right triangles shown below.
round your results to the nearest hundredth as needed.
figure a
image of a right triangle with hypotenuse 6, one leg 4.8, and the other leg x
x =
figure b
image of a right triangle with one leg 11, another leg 8, and hypotenuse x
x =

Explanation:

Step1: Figure A: Identify hypotenuse

The hypotenuse is 6, so apply Pythagorean theorem: $x^2 + 4.8^2 = 6^2$

Step2: Figure A: Solve for $x^2$

$x^2 = 6^2 - 4.8^2 = 36 - 23.04 = 12.96$

Step3: Figure A: Calculate $x$

$x = \sqrt{12.96} = 3.6$

Step4: Figure B: Identify hypotenuse

The hypotenuse is $x$, so apply Pythagorean theorem: $x^2 = 8^2 + 11^2$

Step5: Figure B: Solve for $x^2$

$x^2 = 64 + 121 = 185$

Step6: Figure B: Calculate $x$

$x = \sqrt{185} \approx 13.60$

Answer:

Figure A: $x = 3.6$
Figure B: $x \approx 13.60$