a ski slope on a mountian has an angle of elevation of 25.2 degrees. the vertical height of the slope is 1808 feet. how long is the slope?
No - you should have done 1808/.4257 and get 4246.33.
This is using your trig function.
sine = opposite/hypotenuse
In this problem, we are finding the hypotenuse. Think of the mountain as a right triangle.
sin(25.2) = 1808/x and you are solving for x.
i tried doing that but my hypotenuse was smaller then my opposite... is that ok...
sin(25.2)= .4257 then i divided by 1808 to get x by itself and i got...
2.3535 E -4
wouldn't that be wrong?
We use sine = opp/hyp
Let x be the height of the slope that we are seeking.
sin(25.2 degrees) = 1808 feet/x
Multiply both sides by x and we get:
sin(25.2 degrees)(x) = 1808 feet
Next: Divide both sides by sin(25.2 degrees) to find x.
x = 1808 feet/sin(25.2 degrees)
x = ????
Can you finish?
You know that it is a right triangle and so you already have two angles. So you would find the last (90-25.2) and use the trig functions to find the answer on that missing angle.
Why did the mountain become popular among skiers?
Because it had great "slope-peal"! Now, let's calculate the length of the slope.
To find the length, we can use the trigonometric function tangent (tan). The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the slope (1808 feet), and the adjacent side is the length of the slope.
So, we can set up the equation: tan(25.2 degrees) = 1808 feet / x, where x represents the length of the slope.
Now, let's calculate it using math instead of slopes, shall we? Solving for x, we have:
x = 1808 feet / tan(25.2 degrees)
Calculating this gives us:
x ≈ 1808 feet / 0.464
x ≈ 3897.6 feet
Therefore, the length of the slope is approximately 3897.6 feet. That's quite a descent!
To find the length of the slope, we can use trigonometry. Specifically, we can use the concept of a right triangle and the trigonometric function tangent.
In this case, the angle of elevation of 25.2 degrees is the angle between the ground and the slope. The vertical height of the slope is 1808 feet. We need to find the length of the slope, which represents the hypotenuse of a right triangle.
To find the length of the slope, we can use the tangent function, which is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
The formula to calculate the length of the slope is as follows:
Length of the slope = vertical height / tangent of the angle of elevation
Plugging in the given values:
Length of the slope = 1808 feet / tangent(25.2 degrees)
Now, we need to find the tangent of 25.2 degrees. To do this, we can use a trigonometric calculator or a scientific calculator with a "tan" function.
Using a calculator, we find that the tangent of 25.2 degrees is approximately 0.46747.
Now we can substitute this value into the formula:
Length of the slope = 1808 feet / 0.46747
Evaluating the division:
Length of the slope ≈ 3864.19 feet
So, the length of the slope is approximately 3864.19 feet.