Find the measure of the third side of a right triangle if one leg measures 15 inches and the hypoteneuse measures 17 inches

15 feet.
If this is homework, be sure to show your work.

O^2 + A^2 = H^2 where

Opposite side
Adjacent side
Hypoteneuse

You should be aware that the adjective adjacent has no absolute meaning. It is relative to the angle you are considering.
Let some angle A in a right triangle. Let H be the measure of the hypotenuse. Do not confuse it with some height.
cos(A)=(measure of leg adjacent to A)/H
H= (measure of leg adjacent to A) / cos(A)
However what you call the opposite angle (the other angle I presume), is the complementary of of angle A. Call it angle B
In terms of that second angle
H=(measure of leg adjacent to A)/ sin(B)

What is adjacent to angle A is opposite to the complementary of A.
I think you should work a little more on the meaning of the words adjacent and opposite until you understand that they are relative concepts. They mean nothing until you spell out what angle you are looking at. Without proper understanding of these two concepts you will not be able to use correctly that mnemonic device which you have mangled (BTW)

I do not know it what language you have transcribed the mnemonic , but in English the device is called SOH- CAH-TOA

SOH means: To calculate the Sine of an angle divide the measure of the leg Opposite to the angle by the measure of the Hypotenuse.

CAH means: To calculate the Cosine of an angle divide the measure of the side Adjacent to the angle by the measure of the Hypotenuse.

TOA means: To calculate the Tangent of an angle divide the measure of the side Opposite to the angle by the measure of the side Adjacent to the angle.

Well, just multiply 7.5 by 3. Solution: 22.5

Headlight adjustment is fairly straight forward, you will need to park the car on a level surface with a fence or wall 25 feet away and a reference point for measurements to the right or left of the car. First measure from the reference point to the center line of the car then transfer that to the wall, second, measure from the center of the car to the center of the headlights and transfer those to the wall, third, measure from the ground to the center of the headlights and transfer that to the wall. Once all of the reference points have been transferred, adjust the left (driver's side) headlight so that the most intense part of the beam is 2 inches below and 2 inches to the right of the left mark, the right (passenger side) headlight should be adjusted so that it will be 2 inches below and 1 inch to the left of the mark. If done correctly, you will have very good night vision without blinding oncoming traffic.

P.S. Please note that any heavy objects in the car will be a factor in correct headlight adjustment, have the car loaded as it will be normally used.

in a 45-45-90 triangle, the lengths of the sides are in a ration, 1:1:√2, so if you have one side of the triangle, such as a leg, with the value in the ratio of 1, simply multiply that given number by √2 to get the hypotenuse, if you're instead given the hypotenuse, simply divide by √2 to get the answer for one of the legs. The legs of a 45-45-90 triangle are equal.
I hope this helps!

Hypotenuse being 10 makes the other sides of the triangle 5radical2. Area of a triangle is 1/2*b*h, for an isosceles triangle, it will be 1/2*b*b.
1/2*(5rad2)*(5rad2) 1/2*5*5*rad2*rad2 1/2*25*2 25 cm^2

Double door Fisher is if the Fireplace Series. Pre 1980 stoves had the angle iron welded up the side that became the legs. Grandpa Bear measures 29 1/2 wide and takes up to 24 inch log. Grandma Bear measures 25 1/2 wide, and takes 20 inch log. AFTER 1980 the legs were short and did not extend up the stove corners to top. They were Grandpa Bear III and Grandma Bear III. Very close to the same sizes.

If the distance is 2 cm longer than the short side of a right triangle then the lengths could then be assumed as:
Right triangle A/B = 3 cm
A/C = 1 cm
B/C = 3 cm

Monitor sizes are measured on the diagonal from corner to corner.

A 17" LCD may have a screen width of 12 inches measured from side to side.

If you are measuring a old style CRT monitor (Cathode Ray tube) the visible screen area will be about an inch less as there is about 1/2 inch of plastic frame holding the CRT in the chassis. The manufacturer can advertise the actual size of the screen regardless of how much is actually visible to display information.

If you are talking about software not utilizing all the available screen area to display the image, that is an issue with the people writing the software code not keeping up with the changes in hardware.

In the past year or two, most displays have switched to the 16:9 and 16:10 wide aspect ratios while most web content is still written for the 4:3 old style aspect ratio. Eventually, software developers will catch up with cusrrent hardware.