Answer:
Rotations, reflections and translations.
Step-by-step explanation:
Rotations, reflections and translations are transformations that preserve the both the angle measurements and the lengths of the sides, so congruence is preserved.
Dilations are transformations that keep the angle measurements, but the side lengths change, so the transformation is similar, not congruent.
Answer:
78.5 %
Step-by-step explanation:
the probability = π(2)² / (4×4) ×100%
= 4π /16 × 100%
= π/4 ×100%
= (π×25)%
= 3.14 × 25 %
= 78.5 %
52? ahh thats what im thinking. Maybe wait for someone elses answer
The question is find the height of the tree, given that at two points 65 feet apart on the same side of the tree and in line with it, the angles of elevaton of the top of the tree are 21° 19' and 16°20'.
1) Convert the angles to decimal form:
19' * 1°/60' = 0.32° => 21° 19' = 21.32°
20' * 1°/60' = 0.33° => 16° 20' = 16.33°
2) Deduce the trigonometric ratios from the verbal information.
You can form a triangle with
- horizontal leg x + 65 feet
- elevation angle 16.33°
- vertical leg height of the tree, h
=> trigonometric ratio: tan (16.33) = h /( x + 65) => h = (x+65) * tan(16.33)
You can form a second triangle with:
- horizontal leg x
- elevation angle 21.32°
- vertical leg height of the tree, h
=> trigonometric ratio: tan(21.32) = h / x => h = x * tan(21.32)
Now equal the two expressions for h:
(x+65)*tan(16.33) = x*tan(21.32)
=> x*tan(16.33) + 65*tan(16.33) = x*tan(21.32)
=> x*tan(21.32) - x*tan(16.33) = 65*tan(16.33)
=> x = 65*tan(16.33) / [ tan(21.32) - tan(16.33) ] = 195.73 feet
=> h = 195.73 * tan(21.32) = 76.39 feet.
Answer: 76.39 feet
