A 4-m plank rests against a wall 1.8 m high so that 1.2 m of its projects beyond the wall. Find the angle the plank makes with t
he wall.
this is a trigonometry word problem. please solve after drawing what is said so I can understand.
this is a trigonometry word problem. please solve after drawing what is said so I can understand.
1 answer:
Answer:
50.0°
Explanation:
In the diagram below, line AD represents the plank and line BC represents the wall.
θ is the angle the plank makes with the wall.
<em>Length of the plank on the wall</em>
The plank is 4 m long and 1.2 m extends beyond the wall.
The length of the plank resting on the wall is
AB = 4 – 1.2
AB = 2.8 m
===============
<em>Angle with the wall </em>
Triangle ABC is a right triangle, because the wall is perpendicular to the ground.
cosθ = BC/AB
BC = 1.8 m; AB = 2.8
cosθ = 1.8/2.8
θ = cos⁻¹(1.8/2.8)
θ = cos⁻¹(0.6429)
θ = 50.0°
The plank makes an angle of 50.0° with the wall.
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The domain and range are both all real numbers, also known as
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Step-by-step explanation:
All domain really means is what numbers can you plug in and you get number back from your function.
I should be able to plug in any number into 3x+2 and result in a number. There are no restrictions for x on 3x+2.
The domain is all real numbers.
In interval notation that is .
Now the range is the set of numbers that get hit by y=3x+2.
Well y=3x+2 is a linear function that is increasing. I know it is increasing because the slope is positive 3. I wrote out the positive part because that is the item you focus on in a linear equation to determine if is increasing or decreasing.
If slope is positive, then the line is increasing.
If slope is negative, then the line is decreasing.
So y=3x+2 hits all values of y because it is increasing forever. The range is all real numbers. In interval notation that is .