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2 years ago

HELP PLEASE FAST 15 and 16 how to solve PLEASE

Mathematics

2 answers:

Orlov [11]2 years ago

6 0

1) 164

2) 1600

because a^2 + b^2 = c^2 <3

Hoochie [10]2 years ago

5 0

Answer:

15. 6

16. 40

Step-by-step explanation:

Use the formula for pythagorus: c^2 = a^2 + b^2

15. 10^2 = 8^2 + b^2

100 = 64 + b^2

*minus 64 on both sides

36 = b^2

*square root both sides

b = √36 = 6

16. c^2 = 24^2 + 32^2

c^2 = 576 + 1024

c^2 = 1600

*square root both sides

c = √1600 = 40

Hope this helps :)

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================================================

Explanation:

We have a triangle with these side lengths:

a = 10
b = 16
c = x = unknown

Let's assume that b = 16 is the largest side of this triangle.

By the converse of the pythagorean theorem, we need $b^2 < a^2+c^2$ to be true in order for an acute triangle to happen.

So,

$b^2 < a^2 + c^2\\\\c^2 > b^2 - a^2\\\\c > \sqrt{b^2-a^2}\\\\x > \sqrt{16^2-10^2}\\\\x > \sqrt{156}\\\\x > 12.4899959967968 \ \text{(approximate)}\\\\x > 12.5$

Now let's consider the possibility that the missing side x is actually the longest side.

Using the same theorem as before, we would say,

$c^2 < a^2 + b^2\\\\c < \sqrt{a^2 + b^2}\\\\x < \sqrt{10^2 + 16^2}\\\\x < \sqrt{356}\\\\x < 18.8679622641132 \ \text{(approximate)}\\\\x < 18.9\\\\$

We found that x > 12.5 and x < 18.9

This is the same as saying 12.5 < x and x < 18.9

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2 years ago

HELP PLEASE FAST 15 and 16 how to solve PLEASE ​

HELP PLEASE FAST 15 and 16 how to solve PLEASE