This question boils down to this:
"What is the diagonal of a square with a side length of 90 ft?"
The key to this question is the properties of squares.
All of the angles in a square are right, (90°) but that diagonal is going to bisect two of those into 45° angles.
Now we have two triangles, each with angle measures of 45°, 45°. and 90°.
(an isoceles right triangle)
This 45-45-90 tirnalge is one of two special triangles (the other being the 30-60-90) and here is its special property: the sides opposite these angles can be put as x, x, and x√2 respectively. Why? Well, we know that our triangle is isoceles (the congruent base angles ⇔ congruent sides) and so we call those x...by the Pythagorean theorem...a² + b² = c²...2x² = c²...x√2 = c!
In our case here, that diagonal, being the hypotenuse of our triangle, is going to be 90√2 feet, or approximately 127.3 feet.
Answer:
-0.2
Step-by-step explanation:
Gradient/slope = 
Answer:
∠C' = 66°
Step-by-step explanation:
Because triangles ABC and A'B'C' are similar, their angles are still the same; only their side lengths are different, though still proportionate.
Hence, ∠A = ∠A', ∠B = ∠B', and ∠C = ∠C'.
Here, we're given that ∠A = 68, which means ∠A' = 68; we also know that ∠B = 46, so ∠B' = 46.
We want to find C', so remember that all angles in a triangle sum to 180:
∠A' + ∠B' + ∠C' = 180
68 + 46 + ∠C' = 180
114 + ∠C' = 180
∠C' = 66°
Answer: 
Required theorem:
Pythagorean theorem = 
In other words, one side length squared + another side length squared = the middle lined squared.
Step-by-step explanation:
We can only have a positive distance so your final answer is :
(0,9) just did this problem :^)
