Answer:
The angle of elevation of the sun is 33.7⁰
Step-by-step explanation:
let the height of the tree, T = 10 foot
length of the shadow created by the tree, B = 15 feet long
Height of the tree and the shadow of the tree forms a right angle triangle with the remaining side that joins the two which is known as hypotenuse.
Let the remaining side, hypotenuse, L = ?
Apply Pythagoras theorem;
L ² = T² + B²
L ² = 10² + 15²
L ² = 325
L = √325
L = 18.03 ft
The angle of elevation of the sun, is the angle facing the height of the tree with the length of the shadow of the tree as adjacent of the triangle.
Let the angle of elevation = θ
tan θ = opp / adj
tan θ = 10 / 15
tan θ = 0.66667
θ = tan ⁻¹ (0.66667)
θ = 33.7⁰
Therefore, the angle of elevation of the sun is 33.7⁰
There are two ways to do this.
The first is you plug in the x-value from the point in the table and see if that gives you the y-value from the same point.
For example, your first point is (5,49), so plug in x=5:
y = -5(5)+2 = -25+2 = -23
Since that's not the y-value in (5,49), then (5,49) is not a solution for the equation.
The other option is you plug in both the x-value and the y-value to see if you get a true statement. (A solution will make the equaiton a true statement.)
For example, the first point is (5,49), so you'd plug in x=5 and y=49:
49 = -5(5)+2
49 = -25 + 2
49 = -23
Since that's not true, (5,49) is not a solution.
You'll notice you're basically doing the same thing, it's just whether you plug in one value or both and that's your choice.
Answer:
1/2
Step-by-step explanation:
Because the solid triangle results in a smaller dashed triangle after the dilation, its scale factor will be a fraction. The length of the top side is 2 on the dashed triangle. It corresponds to the top side of the solid triangle which is 4.
2/4 = 1/2
The scale factor is 1/2 the size.
