To prove that triangles TRS and SUT are congruent we can follow these statements:
1.- SR is perpendicular to RT: Given
2.-TU is perpendicular to US: Given
3.-Angle STR is congruent with angle TSU: Given.
4.-Reflexive property over ST: ST is congruent with itself (ST = ST)
From here, we can see that both triangles TRS and SUT have one angle of 90 degrees, another angle that they both have, and also they share one side (ST) ,then:
5.- By the ASA postulate (angle side angle), triangles TRS and SUT are congruent
Answer:
w = 21.4 ft
Step-by-step explanation:
Area of Trapezoid = Area = (a+b)/2 * h
Where a and b are the bases of trapezoid, and h is the height.
In the figure we are given:
a= 32.3 ft
b=w=?
h= 22.9 ft
Area = 614.865 ft²
Putting values in formula
Area = (a+b)/2 * h
614.865 = (32.3 + w) / 2 * 22.9
1229.73 = 32.3 + w * 22.9
1229.73 / 22.9 = 32.3 +w
53.7 -32.3 = w
=> w = 21.4 ft
X = 13
( x + 4) / 51 = (2x - 7) / 57
585 = 45x
585/45 = 45x/45
x = 13
Answer:
The rectangular coordinates of the point are (3/2 , √3/2)
Step-by-step explanation:
* Lets study how to change from polar form to rectangular coordinates
- To convert from polar form (r , Ф) to rectangular coordinates (x , y)
use these rules
# x = r cos Ф
# y = r sin Ф
* Now lets solve the problem
∵ The point in the rectangular coordinates is (√3 , π/6)
∴ r = √3 and Ф = π/6
- Lets find the x-coordinates
∵ x = r cos Ф
∵ r = √3
∵ Ф = π/6
∴ x = √3 cos π/6
∵ cos π/6 = √3/2
∴ x = √3 (√3/2) = 3/2
* The x-coordinate of the point is 3/2
- Lets find the y-coordinates
∵ y = r sin Ф
∵ r = √3
∵ Ф = π/6
∴ y = √3 sin π/6
∵ sin π/6 = 1/2
∴ y = √3 (1/2) = √3/2
* The y-coordinate of the point is √3/2
∴ The rectangular coordinates of the point are (3/2 , √3/2)
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