The height of the ramp above the ground is 1.55 meters.
The difference between the height of the tree is 33.20 meters
<h3>How to find sides of a right triangle?</h3>
The situation forms a right angle triangle.
Therefore, the height the ramp above the ground can be calculated as follows:
Using Pythagoras theorem,
sin 15 = opposite / hypotenuse
sin 15 = x / 6
cross multiply
x = 6 sin 15
x = 6 × 0.2588190451
x = 1.55291427062
x = 1.55
Therefore, the height of the ramp above the ground is 1.55 meters
tan 36 = opposite / adjacent
tan 36 = x / 60
x = 60 tan 36
x = 43.5925516803
x = 43.60 meters
tan 52 = y / 60
60 tan 52 = y
y = 76.7964979316
y = 76.79 meters
The difference between the height of the tree = 76.79 - 43.60 = 33.20 meters
learn more on right triangle here: brainly.com/question/8036473
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Answer:
The coordinates of the final image of point C under
this composition of transformations will be (-3,6).
Therefore, the option B is correct.
Step-by-step explanation:
<u><em>The rule of 90 degree counterclockwise rotation about the origin</em></u>
- When we rotate a figure of 90° counterclockwise about the origin, each point of the given figure or original object gets changed from
to 
.
So when triangle ABC with vertices A(1,1), B(2,4) and C(3,1) is rotated 90°
counterclockwise about the origin, observe the transformation of
the point C(3,1):
P(x, y) → P'(-y, x)
C(3,1) → C'(-1,3)
And then translated using (x,y) → (x - 2, y + 3). So,
(x,y) → (x - 2, y + 3)
C'(-1,3) → C''(-1 - 2, 3 + 3) = C''(-3, 6)
So, the coordinates of the final image of point C under
this composition of transformations will be (-3,6).
Therefore, the option B is correct.
With the center and the point (-6,2) you can deduce the equation of the circle
(x-xo)^2 + (y-yo)^2 = r^2
(x+3)^2 + (y-4)^ = r^2
r^2 is otained from the center and the point (-6,2)
r^2 = (-6 -(-3))^2 + (2-4)^2 = (-6+3)^2 + (-2)^2 = (-3)^2 + 4 = 9 + 4 = 13.
Then the equation of the circle is
(x+3)^2 + (y-4)^ = 13
Now we subsitute the point (10,4) into that equation and see whether it belongs to it:
(10+3)^2 + (4-4)^2 = 13^2
13^2 ≠ 13, so the point does not belong to the equation.
Answer:
14.a
15.c
16.d
Step-by-step explanation:
i choose these because they are in the geometry book
Ah, this my friend, is actually easier than it looks. I promise. Sort of. XD
Alright, so let's start with the basics. You have two shapes that look congruent, and obviously ARE congruent, but how they are congruent can be different.
HIJ (Shape 1) is congruently equal to (~=) shape LKJ (The order does indeed matter) by what?
Well, in terms of congruency, you have about 8 different ways, I only remember 4.
SSS (Side, Side, Side)
SAS (Side, Angle, Side)
ASA (Angle, Side, Side)
AAA (Angle, Angle, Angle)
This means that whichever it is, each must be identified as congruent to the other. If it's SAS, you must know, for certain (not you personally, you can guess, but that's not what they want, they want you to know based on the info they give you) that there are 2 sides that are congruent, and 1 angle that are congruent. Same for all the others, just plug and play.
In the text, this question mentions that side HJ is congruently equal to JL. This means you have 1 set of sides identified as congruent.
The text ALSO mentions that angle H is also congruently equal to angle L. This means you now have 1 set of angles that are congruently equal.
So far, you know you have 1 congruent set of sides (S) and One congruent set of angles (A)
Now, you also can see that based on what we already know, HIJ extends to LKJ, meaning the other angle would ALSO be congruent.
This leaves you with "ASA" (Angle, Side, Angle), meaning 2 sets of angles are congruent, and 1 set of sides.
Your answer is A
~Hope this helps!
