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icang [17]
3 years ago
10

Find the length of the third side. If necessary, write in simplest radical form.

Mathematics
2 answers:
Mazyrski [523]3 years ago
6 0

Answer:

\boxed {\boxed {\sf 8}}

Step-by-step explanation:

This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.

a^2+b^2=c^2

Where <em>a</em> and <em>b </em> are the legs of the triangle and <em>c</em> is the hypotenuse.

In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:

a= 7 \\b= \sqrt{15}

Substitute these values into the formula.

(7)^2+(\sqrt{15})^2=c^2

Solve the exponents.

  • (7)²= 7*7=49

49+ (\sqrt{15})^2=c^2

  • (√15)²=√15*√15=15

49+15=c^2

Add.

64=c^2

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

\sqrt{64}=\sqrt{c^2} \\\sqrt{64}= c\\8=c

The third side length is <u>8.</u>

muminat3 years ago
3 0

Answer:

8

Step-by-step explanation:

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