Since there is no distance between the pole and the base of the tower, we can assume that the pole is at the base of the tower.
We can create a right triangles between the pole and its shadow and between the tower and its shadow as shown in the figure. Let
be the height of the tower. Since our triangles are similar the ratio between its sides is going to be proportional, so we can establish a proportion to find
:
We can conclude that the tower is 137.27 meters tall.
Step-by-step explanation:
The Triangle Sum Theorem states that the interior angles of a triangle add up to 180 degrees. A square for an angle symbolizes that the angle is 90 °, as is the case with angle ∠ACB.
Therefore, as ∠CAB = 2x and ∠ABC = 3x, and angles ∠ACB, ∠CAB, and ∠ABC make up the interior angles of the triangle, we can say that ∠ACB + ∠CAB + ∠ABC = 180, so 90 + 2x + 3x = 180
90 + 2x + 3x = 180
90 + 5x = 180
subtract 90 from both sides to separate the x and its coefficient
5x = 90
divide both sides by 5 to separate the x
x = 18
(a) ∠CAB = 2x = 18(2) = 36
(b) ∠ABC = 3x = 18(3) = 54
(c) Any triangle with a 90° angle is called a right triangle. This has a 90° triangle, and is therefore a right triangle. Similarly, a 90° angle in a triangle is called a right angle.
Answer:
(4k^2+7)(7k+6)
Step-by-step explanation:
1. group the first two terms (28k^3-24k^2). The greatest common factor is 4k^2. If you factor that out you get 4k^2(7k-6)
2.When you group the last two terms (49k-42). you can factor out a 7.
7(7k-6).
3. There is a (7k-6) in both sections so you can combine all the terms.
4k^2(7k-6) 7(7k-6) becomes (4k^2)(7k-6)
Answer:
3
Step-by-step explanation:
9 divide by 3 is 3 itself so the answer is 3
