HELP PLEASE THERE ARE TWO MORE.
2 answers:
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Answer:
Yes, It is a right triangle for the given vertices.
Step-by-step explanation:
Given:
Q(7, –10),
R(–3, 0),
S(9, –8)
To Find:
determine whether is a rig ht triangle for the given vertices = ?
Solution:
QR=
QR=
QR=
QR=--------------------------(1)
QR=14.142136
RS=
RS=
RS=
RS=---------------------------(2)
RS=14.422205
QS=
QS=
QS=
QS=-------------------------------------(3)
QS=2.828427
According to Pythagorean Theorem,
Substituting the values,
208 = 208
Pythagorean theorem is satisfied. Hence it is a right triangle.
<h3>Answer: point Q is located at (-1, 1)</h3>
=================================================
Explanation:
Check out the diagram below.
Plot R(-3,7) and T(3,-11) on the same xy grid.
Draw a vertical line through R and a horizontal line through T. A right triangle forms. At the intersection point is point S(-3,-11)
----------------------
Now measure the distance from point S to point T. You can count out the spaces or subtract the x coordinates and use absolute value.
|x1-x2| = |-3-3| = |-6| = 6
From point S to point T is 6 units.
We want to subdivide this horizontal length in the ratio 1:2
What this means is that we want to plot a point U somewhere such that SU:UT = 1:2
In other words,
SU = x
UT = 2x
SU+UT = ST
x+2x = 6
3x = 6
x = 6/3
x = 2
So we must move 2 spaces to the right from point S to get to U(-1,-11)
Going from point U(-1,-11) to T(3,-11) is 4 spaces
We have SU:UT = 2:4 = 1:2 to help confirm we have the correct location for point U
From point U, we then move straight up to the line segment RT
We'll land on Q(-1,1)
----------------------
Another way to find the y coordinate of point Q is to subdivide the segment RS into the ratio 1:2 similar to how we divided ST up
Segment RS is 18 units long since we go from y = 7 to y = -11 when going from R to S.
If V was on segment RS such that
RV:VS = 1:2
and RV = y
then
RV+VS = RS
y+2y = 18
3y = 18
y = 6
RV = y = 6
VS = 2y = 2*6 = 12
So you'll move 6 units down from y = 7 to land on y = 1 (when going from the y coordinate of R to the y coordinate of Q)
Answer:
A. height from truck to platform = 28 ft
B. length of the start of the conveyor to the end of the conveyor = 70 ft
C. If the height of the truck to the platform is 37.5 ft, the angle of elevation = 30°
Step-by-step explanation:
Consider the sketch of the problem attached below.
based on the laws of trigonometry, we can recall that
sin θ =
in this case, we are looking for the opposite side of the triangle.
hence we have, opposite side = 75 × sin 22
=28.095 ft ≈ 28 ft
as shown in the sketch, this opposite side is the height of the truck from hte platform
B Similarly, from the laws of trigonometry, the adjacent side of the triangle can be obtained using the relation
cos θ =
Adjacent side = hypotenuse side × cos θ
Adjacent side = 75 ×cos (22)
Adjacent side = 69.53 ≈ 70 ft
C. If the new height of the truck to the platform is now 37.5 feet, the problem is redrawn in sketch 2. However, the same formulas still apply.
Sin θ =
Sin θ = = 0.5
θ = ( 0.5)
θ = 30°
