Answer:
12. 6.4
13. 20
Step-by-step explanation:
This is the Pythagorean theorem, which says a^2+b^2=c^2. So for problem 12 we have 4^2+5^2=c^2. Since, 16+25=41, c=sqrt41 which is about 6.4. For problem 13 we have 15^2+b^2=25^2. Since 25^2-15^2=400, b=sqrt400 which is 20. Hope this helps!
Answer:
12. 6.4
13. 20
Step-by-step explanation:
Mathematics: Define and explain.
This is a right triangle, so the Pythagorean Theorem applies.
The Pythagorean Theorem states that the sum of the squared side lengths of a right triangle must equal the hypotenuse when squared.
The legs of a triangle are the sides that form the right angle.
The hypotenuse is the longest side; the hypotenuse is always diagonal from the small square indicating a right angle.
[tex]a^2+b^2=c^2[/tex]
[tex]a,b-legs[/tex]
[tex]c=hypotenuse[/tex]
Mathematics: Solve.
In the first triangle, the missing side length is the hypotenuse.
[tex]5^2+4^2=c^2[/tex]
[tex]25+16=c^2[/tex]
[tex]c^2=41[/tex]
**41 IS NOT A PERFECT SQUARE. THEREFORE, I MUST ROUND THE SQUARE ROOT TO THE NEAREST TENTH.**
[tex]6.40312424[/tex] ≈ [tex]6.4[/tex]
[tex]c=6.4[/tex]
Hence, the hypotenuse, c, is equal to 6.4.
In this second triangle, we are solving the find one of the legs.
[tex]15^2+b^2=25^2[/tex]
[tex]225+b^2=625[/tex]
[tex]625-225=400[/tex]
[tex]b^2=400[/tex]
[tex]b=20[/tex]
Hence, one of the legs, b, is equal to 20.
Mathematics: Conclude.
12) The missing side is equal to 6.4 when rounded to the nearest tenth.
13) The missing side is equal to 20.
