please po help me.
A chimney projects 6 feet above the roof. At a point 10 feet 8 inches down the roof from the base of the chimney,the chimney subtends an angle of 17°40' . find the angle at which the roof is inclined to the horizontal.
draw a diagram. extend the chimney downward to where it meets a horizontal line drawn from the point Q 10'8" down the roof. Label
T = top of chimney
B = bottom of chimney
PQ = base of right triangle TPQ.
using the law of sines,
6/sin17°40' = 10'8"/sinT
sinT = 10.666*sin17°40'/6 = 0.5395
T = 32.65°
So, in triangle TBQ, angle B = 129.68°
Thus, the angle of the roof (BQP) is
90-(180-129.68) = 39.68°
Call it 40°
Well, well, well, looks like we have a puzzler here! Alright, let's break it down. We have a chimney, we have a roof, and we have some angles.
First off, we need to find the angle at which the roof is inclined to the horizontal. Now, if we take a good look at the situation, we can see that the chimney is sticking up and the roof is sloping down. It's like they're playing a game of seesaw, but without the fun.
Now, if we draw a little triangle, we'll have the chimney as one side, the roof as another side, and the imaginary horizontal line as the base. The angle we're looking for is the one between the roof and the horizontal line.
To find this angle, we have to do some trigonometry... oh joy! We know that the chimney projects 6 feet above the roof, and at a point 10 feet 8 inches down the roof from the base of the chimney, the chimney subtends an angle of 17°40'.
Are you still following me? Great! Now, we can use some good ol' tangent to solve this riddle. We have the opposite side (6 feet) and the adjacent side (10 feet 8 inches), so we can use the formula tangent(angle) = opposite/adjacent.
Let's convert that pesky 10 feet 8 inches to just inches, which gives us 128 inches. Now, we can calculate the tangent of the angle. Hold your breath, here comes the answer!
The tangent of 17°40' is approximately 0.3174. Now, all we have to do is find the inverse tangent (also known as the arctangent) of 0.3174, and voila! That will give us the angle we're after.
So, my dear friend, after plugging that number into a calculator, we find that the angle at which the roof is inclined to the horizontal is approximately 17.53 degrees.
Phew! That was a long journey, but we made it! I hope my funny little explanation helped you out. If not, don't worry, I'm here to make you smile, even if math makes you frown.
To find the angle at which the roof is inclined to the horizontal, we can use trigonometry.
Let's first convert 10 feet 8 inches to inches. Since there are 12 inches in a foot, we have:
10 feet 8 inches = (10 x 12) + 8 = 128 + 8 = 136 inches.
Now, let's set up a right-angled triangle to represent the situation. The vertical side of the triangle represents the chimney, which is 6 feet tall. The horizontal side represents the distance from the base of the chimney to the point on the roof, which is 136 inches.
Let's call the angle at which the roof is inclined to the horizontal "θ".
In the triangle, we have:
Opposite side = height of chimney = 6 feet
Adjacent side = distance on the roof = 136 inches
We know that tangent (tan) of an angle is equal to the ratio of the opposite side to the adjacent side.
So, we can write:
tan(θ) = opposite/adjacent
tan(θ) = 6/136
Now, we can solve for θ by taking the inverse tangent (arctan) of both sides:
θ = arctan(6/136)
Using a calculator, we get:
θ ≈ 2.50 degrees
Therefore, the angle at which the roof is inclined to the horizontal is approximately 2.50 degrees.
To find the angle at which the roof is inclined to the horizontal, we can use trigonometry.
Let's represent the angle at which the roof is inclined to the horizontal as α.
We have a right triangle formed by the roof, the chimney, and the vertical line connecting the top of the chimney to the roof. The height of the chimney can be represented by h, and the distance from the base of the chimney to the point on the roof as d.
Given:
Height of the chimney, h = 6 feet
Distance from the base of the chimney to the point on the roof, d = 10 feet 8 inches = 10.67 feet
We know that:
Tan(α) = Opposite / Adjacent
In this case, the "opposite" side is the height of the chimney (h), and the "adjacent" side is the distance from the base of the chimney to the point on the roof (d).
So, we have:
Tan(α) = h / d
Substituting the given values:
Tan(α) = 6 / 10.67
Now, to find α, we can apply the inverse tangent function (also known as arctan) to both sides of the equation:
α = arctan(Tan(α)) = arctan(6 / 10.67)
Calculating this (using a calculator or an online trigonometric calculator) will give us the value of α, which represents the angle at which the roof is inclined to the horizontal.