Given the side lengths below, which would not create a right triangle? A. 5, 12, 13 B. 8, 15, 17 C. 6, 8, 10 D. 5, 10, 15
1 answer:
You might be interested in
One system of equations would be
L = w+4
H = w-10
4H + 8(wL) = 1544
There is one viable solution; the width is 12, the length is 16, and the height is 2.
Using substitution with the system of equations, we have
4(w-10)+8(w(w+4))=1544
4w-40+8(w²+4w)=1544
4w-40+8w²+32w=1544
Combining like terms, we have
8w²+36w-40=1544
Factoring out a 4, we have
4(2w²+9w-10)=1544
Dividing both sides by 4 gives us
2w²+9w-10=386
Subtract 386 from both sides to get
2w²+9w-396=0
Using the quadratic formula, we have
Since a negative width makes no sense, we know that w=12.
This means L=w+4=12+4=16 and H=w-10=12-10=2
L = w+4
H = w-10
4H + 8(wL) = 1544
There is one viable solution; the width is 12, the length is 16, and the height is 2.
Using substitution with the system of equations, we have
4(w-10)+8(w(w+4))=1544
4w-40+8(w²+4w)=1544
4w-40+8w²+32w=1544
Combining like terms, we have
8w²+36w-40=1544
Factoring out a 4, we have
4(2w²+9w-10)=1544
Dividing both sides by 4 gives us
2w²+9w-10=386
Subtract 386 from both sides to get
2w²+9w-396=0
Using the quadratic formula, we have
Since a negative width makes no sense, we know that w=12.
This means L=w+4=12+4=16 and H=w-10=12-10=2
As you can see in the picture, the ladder leaning against the wall makes a right triangle with the sides being the wall, the ground and the ladder. The ladder is opposite the right angle and so is the hypotenuse (the longest side of the triangle). The angle between the ladder and the ground is labeled a.
We know the height of the ladder (10 feet) and also the height off the ground of the windowsill (8.5 feet). That second side is opposite the angle a. So, when we consider angle a we know the length of the side opposite and of the hypotenuse.
Recall the sin of an angle can be found by using (opposite/hypotenuse).
So we have: sin a = 8.5 / 10. That is, sin a = .85
We are looking for the angle whose sin is .85 and can find this using the inverse sin function.
a is approximately 58.211669 degrees which is less than the 65 degrees and so safe.
Just to be on the safe side, I remind you that your calculator must be in degrees (not radians) to do this problem.
We know the height of the ladder (10 feet) and also the height off the ground of the windowsill (8.5 feet). That second side is opposite the angle a. So, when we consider angle a we know the length of the side opposite and of the hypotenuse.
Recall the sin of an angle can be found by using (opposite/hypotenuse).
So we have: sin a = 8.5 / 10. That is, sin a = .85
We are looking for the angle whose sin is .85 and can find this using the inverse sin function.
a is approximately 58.211669 degrees which is less than the 65 degrees and so safe.
Just to be on the safe side, I remind you that your calculator must be in degrees (not radians) to do this problem.