The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if necessary. legs: 28 in. and 15 in.

A. 31.8 in.

B. 37.5 in.

C. 23.6 in.

D. 29.6 in.

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A. 31.8 in.

B. 37.5 in.

C. 23.6 in.

D. 29.6 in.

Step-by-step explanation:

Length of third side

[tex]= \sqrt{ {24}^{2} + {16}^{2} } \\ = \sqrt{576 + 256} \\ = \sqrt{832} \\ = 28.84 \\ \approx \: 28.8 \: in[/tex]

Or

Length of third side

[tex]= \sqrt{ {24}^{2} - {16}^{2} } \\ = \sqrt{576 - 256} \\ = \sqrt{320} \\ = 17.8885438 \\ \approx \: 17.9 \: in[/tex]

The answer is 32

Step-by-step explanation:

[tex]a^{2}= b^{2} + c^{2}[/tex]

[tex]a= \sqrt[2]{a^{2} +c^{2} }[/tex]

[tex]a= \sqrt[2]{20^{2} +25^{2} }[/tex]

[tex]a= \sqrt[2]{1025 }[/tex]

a = 32.02

it's B 28.8 in

Step-by-step explanation:

The answer is C. 28.8 in

Step-by-step explanation:

Given a=16 and b=24,

c = 28.84441 = 8√13

∠α = 33.69° = 33°41'24" = 0.588 rad

∠β = 56.31° = 56°18'36" = 0.98279 rad

h = 13.3128

area = 192

perimeter = 68.84441

inradius = 5.57779

circumradius = 14.42221 = 4√13

The answer is 50.2 m

Step-by-step explanation:

Given a=34 and b=37,

c = 50.24938

∠α = 42.58° = 42°34'50" = 0.74317 rad

∠β = 47.42° = 47°25'10" = 0.82763 rad

h = 25.03514

area = 629

perimeter = 121.24938

inradius = 10.37531

circumradius = 25.12469

B. 13.2 m

Step-by-step explanation:

Using the Pythagorean theorem, which is a^2 + b^2 = c^2, you can substitute in 9 for a and 16 for c. This puts it at 9^2 + b^2 = 16^2, which equals 81 + b^2 = 256. Subtract 81 from both sides to get b^2 = 175. Take the square root of both sides to get b = sqrt 175. The sqrt of 175 rounded to the nearest tenth is 13.2

Use Pythagorean Theorem:

28^2+15^2=c^2

1009=c^2

Square both sides:

31.8

A

32^2 + x^2 = 38^2

1024 + x^2 = 1444

-1024 -1024

x^2= 420

x=20.493901532

14.6

Explanation:

You need the equation [tex]a^{2} +b^{2} = c^{2}[/tex]

both legs can be "a" or "b" the hypotenuse is "c"

insert what you know in this equation then solve for the unknown.

[tex]34^{2} +b^{2} = 37^{2} \\1156+b^{2} = 1369\\b^{2}=213\\[/tex]

now to cancel out the square you take the square root of both sides giving you: 14.6

A)24.8in

Step-by-step explanation:

17^2 + 18^2 =613

sq root of 613 = 24.758...

24.8in