If θ = 58° and p = 150 in, what is the value of n to the nearest tenth of an inch?
Well, n is a bit of a mystery here, isn't it? It's like trying to find a clown's shoe in a haystack! But fear not, I'm here to help. Now, I don't have a crystal ball, but I do know a thing or two about trigonometry. To find n, we can use the equation n = p * cos(θ). Plugging in the values you gave, we have n = 150 * cos(58°). Now, if I had a magic wand, I'd wave it and give you the answer right away. But since I don't, let me crunch the numbers. *beep boop beep* Ah, yes! After some calculations, n is approximately 74.7 inches. So grab your measuring tape and get ready for some handy work!
To find the value of n, we can use the trigonometric function called tangent (tan). The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, we have the angle θ and the adjacent side p.
The formula for tangent is:
tan(θ) = Opposite / Adjacent
From the given problem, we know that θ = 58° and p = 150 in. Plugging these values into the formula, we get:
tan(58°) = n / 150
Now, to solve for n, we need to isolate it. We can do this by cross-multiplying:
n = tan(58°) * 150
Using a scientific calculator, we can find the value of tangent(58°):
tan(58°) ≈ 1.664279481
Plugging this value into the equation, we get:
n ≈ 1.664279481 * 150
Simplifying the calculation:
n ≈ 249.6419221
Rounding to the nearest tenth of an inch, we get:
n ≈ 249.6 inches
Therefore, the value of n to the nearest tenth of an inch is approximately 249.6 inches.
To find the value of n, we can use the trigonometric relationship of a right triangle which states that the tangent of an angle is equal to the length of the side opposite the angle (n) divided by the length of the side adjacent to the angle (p):
tan(θ) = n / p
Given that θ = 58° and p = 150 in, we can substitute these values into the equation:
tan(58°) = n / 150
Now we can solve for n by isolating it:
n = tan(58°) * 150
Using a calculator, we can evaluate that:
n ≈ 215.11
Therefore, the value of n to the nearest tenth of an inch is approximately 215.1 in.