Pythagorean Theorem

[Goodstudent]

Hi,
I'm doing my homework and I happen to come across the problem:

Television srceen size is measured on the diagonal. What is the height of this screen? Round your answer to the nearest tenth.

It shows a trangle with: 42 on the longest side(with slants in the towards the left side), 37.5 on the bottom of the figure, and h on the right side on the figure.

How do I solve this and what is the formula?

 

[mmm4444bot]

You already typed the name of the formula, in your subject line.

The triangle is a right triangle because the base and height (legs) are perpendicular.

The longest side is called the hypotenuse.

The Pythagorean Theorem relates the three sides of any right triangle.

a^2 + b^2 = c^2

a is the length of one leg, b is the length of the other leg, and c is the hypotenuse.

In other words, you square the length of each leg and add the squares. That sum always equals the square of the hypotenuse.

The base of the screen is 37.5 and the hypotenuse is 42.0; the height is unknown, so we need a symbol to represent it.

Let h = the height of the screen

Now write the Pythagorean Theorem, using the given lengths.

(37.5)^2 + h^2 = (42.0)^2

Can you finish it ?

 

[Goodstudent]

Well i know 37.5^2 is 1406.25 and 42^2 is 1,764 but how exacally would i solve for h^2?

 

[Goodstudent]

My choices to the nearest tenth
a.4.5 (20.25)
b. 9.0 (81)
c.18.9 (375.21)
d.20.3 (412.09)

I squared each one
Added a^2 (1406) + b^2 (1743.46) = c^2 (1764)

The answer is c

Please let me know if I did this right.

 

[mmm4444bot]

For pre-algebra, yes, your process is okay.

In algebra, we solve the equation using steps to isolate h.

37.5^2 + h^2 = 42^2

Do exponents first

1406.25 + h^2 = 1764

Subtract 1406.25 from each side

h^2 = 357.75

Take the square root of each side

h = 18.91428

 

[Goodstudent]

I understand now. Thanks!