Answer:
The required drawing showing the cliff, river, and tower as well as the details in the question is attached, please find alongside the answer
The width of the river is approximately 51.55 meters
Step-by-step explanation:
The height of the observation tower = 11 meters
The angle of elevation of the cliff top and the opposite side of the river = 20°
The angle of elevation of the tower top and the opposite side of the river = 30°
Therefore, by sine rule, we have;
h/sin(20) = w/sin(60)
11/sin(10) = length, l/sin(60)
l = sin(60) ×11/sin(10) ≈ 54.86 meters
w = l × cos (20) = 54.86 meters × cos (20) ≈ 51.55 meters
The width, w, of the river is approximately 51.55 meters.
Answer:
5.7 units
Step-by-step explanation:
The distance from point P to QS is the distance from point P (1, 1) to the point of interception R(-3, 5).
Use distance formula to calculate distance between P and R:
Let,
Plug in the values into the formula.
(to nearest tenth)
Answer:
0.8
Step-by-step explanation:
80p= 80/100
8/10
4/5
0.8
Answer:55.56
Step-by-step explanation:
Answer:
3.15
Step-by-step explanation:
Let the unknown number be n.
Then 12n = √n + 36
We must eliminate the √ operator. One way to do this is to replace √n temporarily with x. Then 12n = 12x^2, and we have 12x^2 - x - 36 = 0. This is a quadratic with a= 12, b= -1 and c = -36
Solving for x using the quadratic formula:
1 plus or minus √(1 - 4(12)(-36)
x = ----------------------------------------------
2(12)
1 plus or minus √1729
x = -----------------------------------
24
1 plus or minus 41.58
x = -----------------------------------
24
Since x = √n, n must be a positive number. Thus,
1 + 41.58
x = ---------------- = 1.77
24
If x = 1.77 = √n, then n = 1.77^2 = 3.15.
Check: Is this true? A number multiplied by 12 is equal to the sum of the square root of that same number and 36.
12(3.15) = √3.15 + 36, or
37.8 = 1.77 + 36 = 37.77 This checks out.
The number is 3.15
