Answer:
c = 13
m∡A = 60°
m∡B = 30°
Step-by-step explanation:
This is a 5-12-13 triangle. However, to make sure, I will put the steps.
Allow for each sides to be denoted as a-b-c, in which c is the hypotenuse (longest side). Set the equation:
a² + b² = c²
Plug in the corresponding numbers to the corresponding variables:
5² + 12² = c²
Simplify. First, solve the exponents, and then add:
(5²) = 5 * 5 = 25
(12²) = 12 * 12 = 144
25 + 144 = c²
c² = 169
Note the equal sign, what you do to one side, you do to the other. Isolate the variable, c, by rooting both sides:
√c² = √169
c = √169 = √(13 * 13) = 13
c = 13
13 is your answer for c.
Note the measurements of the angles. We know that this is a 30-60-90 triangle, and so it will be easy to figure it out. Note that the corresponding angles will depend on that of the opposite side's measurement lengths. The hypotenuse will always be on the opposite side of the largest angle (as given), as c, the longest side, is opposite of ∡C, which is the largest angle (90°). Based on this information, it means that ∡A would be 60° (as it is opposite of the middle number, 12), and ∡B would be 30° (opposite of the smallest number, 5).
Answer:
11 inches
Step-by-step explanation:
A rectangle's perimeter can be found using:
p=2l+2w
We know that the perimeter, p, is 58, and the length/height is 18. Therefore, we can substitute those values in
58=2(18)+2w
Multiply 2 and 18
58=36+2w
Since we want to find the width, we need to get w by itself. First, subtract 26 from both sides
58-36=36-36+2w
22=2w
Since w is being multiplied by 2, divide both sides by 2. This will cancel out the 2, and leave w by itself.
22/2=2w/2
11=w
So, the width is 11 inches
Yes, the two lines are parallel which makes No solution the correct answer.
