A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. what is the measure of the angle formed between the r
amp and the freeway?
2 answers:
The ramp,the rise and the base, when illustrated, will form a right triangle. The hypotenuse is the ramp which measures 200 ft long. The rise is the vertical height which measures 37 feet. As you can see in the picture, the arc drawn below the ramp to the horizontal line directing to the freeways is the unknown angle that we have to find.
First, we find the angle made between the ramp and the rise (dashed line). Let's denote this is angle α. We make use trigonometric functions like cosine. Cosine of an angle is equal to the ratio of its adjacent side to the hypotenuse. In equation form:
cos α = 37/200, where α is the angle of inclination of the ramp
cos α = 0.185
α =cos^-1(0.185)
α = 79.34°
Next, let's denote the unknown angle as angle β. When you add the right angle and angle α, the sum would be angle β. Therefore,
β = 90° + 79.34°
β = 169.34°
First, we find the angle made between the ramp and the rise (dashed line). Let's denote this is angle α. We make use trigonometric functions like cosine. Cosine of an angle is equal to the ratio of its adjacent side to the hypotenuse. In equation form:
cos α = 37/200, where α is the angle of inclination of the ramp
cos α = 0.185
α =cos^-1(0.185)
α = 79.34°
Next, let's denote the unknown angle as angle β. When you add the right angle and angle α, the sum would be angle β. Therefore,
β = 90° + 79.34°
β = 169.34°
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Answer:
- <u>Option A. about 100.5ft²</u>
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Explanation:
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The <em>surface</em> to paint, of each pillar, is equal to the lateral area of a<em> cylinder </em>with he dimensions given.
The formula for the laeral area of a cylinder is:
Substitute including the conversion factor to convert inches to feet:
Remember that to tell if a function is linear for a table, you should look for a constant rate of change, and the only function that has a constant rate of change is the first one. 
is increasing by 1, and 
is increasing by 0.5.
Now that we know that, lets find the equation of our table.
First, lets take tow points from our table: (1,
) and 
.
Next, use the slope formula:
We know for our points that
, 
,
, and 
, so lets replace those point in our formula to find 
:
Finally, we can use the point slope formula
to find our equation:
We can conclude that the first table represents a linear function, and its equation is
Now that we know that, lets find the equation of our table.
First, lets take tow points from our table: (1,
Next, use the slope formula:
We know for our points that
Finally, we can use the point slope formula
We can conclude that the first table represents a linear function, and its equation is