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Algebra homework questions...Ten points to best answer in 10 minutes!?
Okay, so there a couple of questions...
1. Find the angle of depression from the top of a lighthouse 288 feet above the water level to the water life of a ship 4 miles (21120 feet) offshore. Answer in units of degrees.
2. Find the length of the largest circular track that can be built on a triangular piece of property whose sides are 208 feet, 255 feet, and 325 feet.
3. Container A holds a solution that is 70% alcohol while container B holds a solution that is 10% alcohol. How many liters of the solution in container A are needed to produce 18 liters of a solution that is 60% alcohol?
4. A 113 foot line is attached to a kite. When the kite has pulled the line taut, the angle of elevation to the kite is approximately 57 degrees. Approximate the height of the kite. Answer in units of feet.
Thank you to those who help!
1) tan(theta) = 21120/288
theta = 89.22 degrees
#2)
Given a scalene triangle (no two sides are equal) with sides a, b, c.
The radius of the inscribed circle within the triangle = r = sqrt[(s-a)(s-b)(s-c)/s]
Where s = (a+b+c)/2
So for our problem:
s = (208+255+325)/2 = 394
r = sqrt[(186)(139)(69)/394]
r = 67.3
They aren't asking for the radius though, they are asking for the circumference of the circle so
c = 2*pi*r
c = 2*3.14159*67.3
c = 423 feet
#3)
A + B = 18
0.70A + 0.10B = 10.80
solve for A and B
15 liters of A and 3 liters of B
#4)
113sin(57)
= 94.77 feet
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