To find out whether or not a triangle is a right triangle, you have to figure out whether or not it satisfies the Pythagorean Theorem.
The Pythagorean Theorem says that the sum of the squares of the side lengths, represented by variables a and b, must equal the square of the hypotenuse, represented by c.
a² + b² = c²
20² + 48² = 52²
400 + 2304 = 2704
2704 = 2704
When we plug in the side lengths and simplify the Theorem, it results in a true statement, so we can conclude that yes, the triangle is a right triangle.
Answer:
h = 7.63 ft
Step-by-step explanation:
When a ladder leans against a wall, it forms a right angled triangle. The length of the ladder becomes the hypotenuse of the triangle, while the distance of the bottom of ladder from the wall and the height of top of the ladder from the ground becomes the perpendicular and base, depending upon the selected angle. Using Pythagora's Theorem in this right angled triangle:
Hypotenuse² = Perpendicular² + Base²
where,
Hypotenuse = Length of Ladder = 16 ft
Base = Distance between bottom of ladder and wall = x
Perpendicular = Height of top of of the ladder from ground = x + 6 ft
Therefore,
(16)² = x² + (x + 6)²
256 = x² + x² + 12x + 36
128 = x² + 6x + 18
x² + 6x - 110 = 0
solving the quadratic equation and using positive value:
x = 1.63 ft
So, the height of top of ladder is:
h = 1.63 ft + 6 ft
<u>h = 7.63 ft</u>
Answer:
2.7 is the correct answer
Step-by-step explanation:
Answer:Volume = 108 cm ³
Explanation:For a square pyramid, the volume can be calculated as follows:
Volume =
* area of base * height
Volume =
* side² * height
We have:
side length = 6 cm
height = 9 cm
Therefore:
Volume =
* 36 * 9 = 108 cm ³
Hope this helps :)
The sequence is alternatingly decreasing and increasing.
3 - 9 = -6
-6 + 18 = 12
12 - 8 = 4
4 + 16 = 20
Therefore, next term will be:
20 - 7 = 13
