Answer:
79.1 ft
Step-by-step explanation:
Draw a vertical segment about 3 inches tall. Label the upper endpoint A and the lower endpoint B. That is the cell phone tower. Starting at point B, draw a horizontal segment 1 inch long to the right. Label the right endpoint C. Connect C to A with a segment.
Segment BC is 25 ft long. Segment AB is 75 ft long. Angle B is a right angle.
You are looking for the length of segment AC, the guy wire length.
Triangle ABC is a right triangle with right angle B.
Sides AB and BC are the legs, and side AC is the hypotenuse.
We can use the Pythagorean Theorem:
(leg1)^2 + (leg2)^2 = (hyp)^2
Let one leg be a, the other leg be b, and let the hypotenuse be c.
Then you have
a^2 + b^2 = c^2
We have a = 75 ft
b = 25 ft
We are looking for c, the length of the hypotenuse.
(75 ft)^2 + (25 ft)^2 = c^2
5625 ft^2 + 625 ft^2 = c^2
6250 ft^2 = c^2
c^2 = 6250 ft^2
Take the square root of both sides.
c = 79.0569... ft
Answer: 79.1 ft
So remember that the area of a trapezoid is 
, with b = bases and h = height. Before we can do the equation, however, we have to find the height. Using the right triangle, we can use the pythagorean theorem, which is 
.
Since we know that the hypotenuse is 13 and one of the legs is 12, we can solve for the other leg. Our equation will look like this: 
Firstly, solve the exponents: 
Next, subtract 144 on both sides: 
Next, square root both sides, and your height will be: x = 5
Now that we know both the height, 5, and the bases, 30 and 40, we can solve for the area of the trapezoid. Our equation will look like this: 
Firstly, combine everything on the numerator: 
Next, divide the fraction: 
Next, multiply, and your answer will be A = 175 un^2.
Answer:
b=A/h
Step-by-step explanation:
To isolate b, you need to divide both sides by h. Therefore:
A=bh
b=A/h
Hope this helps!
Answer:
x = 10/27
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
9/5x = 2/3
<u>Step 2: Solve for </u><em><u>x</u></em>
- Divide both sides by 9/5: x = 10/27
<u>Step 3: Check</u>
<em>Plug in x to verify it's a solution.</em>
- Substitute: 9/5(10/27) = 2/3
- Multiply: 90/135 = 2/3
- Simplify: 2/3 = 2/3
And we have our final answer!
