Answer:
- p = 4.5
- u = 35
- w = 12.6
- x = 55
- y = 35
- z = 7.2
Step-by-step explanation:
Angles u° and 55° are the acute angles of a right triangle, so are complementary.
u° = 90° -55° = 35°
Angles x° and y° are corresponding angles with 55° and u°, so are congruent to them, respectively.
x° = 55°; y° = 35°
In summary:
u = 35, x = 55, y = 35
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Corresponding sides of the triangles are proportional, so ...
p/6 = 3/4
p = 18/4 = 4.5 . . . . . multiply by 6
The Pythagorean theorem can be used to find z:
z² = 4² +6² = 52
z = √52 = 2√13 ≈ 7.2
The scale factor between the larger triangle and the smaller one is ...
(3+4)/4 = 7/4
so ...
w = 7/4·z = (7/2)√13 ≈ 12.6
In summary:
p = 4.5; w ≈ 12.6; z ≈ 7.2
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<em>Comment on this problem figure</em>
With the given side measurements, the angles would be more correctly described as 56.3° and 33.7°. The geometry shown cannot exist.
We presume you're to use corresponding side relationships to find the side lengths, and angle relationships to find the angles. Trig relations will relate sides to angles, but those are not needed (or useful) in this problem. Since the angles are not properly related to the sides, trig relationships can only introduce confusion into what is otherwise a straightforward problem.
Answer:
#adult tickets sold = 346
#student tickets sold = 812
Step-by-step explanation:
let 'x' = # adult tickets sold
let 'y' = # students tickets sold
System of Equations:
x + y = 1158
5x + y = 2542
I used the elimination method and multiplied the first equation by -1
-x - y = -1158
+<u> 5x + y = 2542</u>
4x = 1384
x = 346
346 + y = 1158
y = 812
So basically you need to ......
Hope it helps
9514 1404 393
Answer:
a = √(b² +c² -2bc·cos(A))
a = √(c² -b²)
Step-by-step explanation:
For sides a, b, c, and opposite angles A, B, C, the general form of the law of cosines is ...
a² = b² + c² -2bc·cos(A)
An expression for 'a' can be written by taking the square root.
a = √(b² +c² -2bc·cos(A))
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If you recognize that cos(A) = b/c, then a substitution can be made:
a = √(b² +c² -2(bc)(b/c)) = √(b² +c² -2b²)
a = √(c² -b²) . . . . . . . same as the Pythagorean theorem
For this question I’m pretty sure you have to multiply Base X height to find the area of this equation.