Answer: Angles A and B are complementary angles
If Sin A ≈ 0.766 then Cos B ≈ 0.766.
If Cos B ≈ 0.766 then Sin A ≈ 0.766
Step-by-step explanation: In any given right angled triangle, one angle measures 90 degrees while the addition of the other two angles equals to 90 degrees. Hence if angle C is given as 90 degrees, then angles A and B added together equals 90 degrees (complementary angles equal 90 degrees).
Also, Sin A cannot be the same value as Sin B, since angle A and angle B are not equal in measurement. However, being complementary, the Sin of angle A equals the Cos of angle B.
If Sin A ≈ 0.766, then angle A ≈ 50 degrees
That makes angle B equal to 40 degrees. The Cos of B ≈ 0.766
Therefore if Sin A ≈ 0.766, then Cos B ≈ 0.766
If Cos B ≈ 0.766 then Sin A ≈ 0.766 are both correct
Answer:
4x^2 -12x +9 ft^2
Step-by-step explanation:
The area of a square is
A = s^2 where s is the side length
A = (2x-3) ^2
A = (2x-3) (2x-3)
FOIL
first 2x*2x =4x^2
outer 2x (-3) = -6x
inner -3*2x = -6x
last -3*-3 = 9
Add them together
4x^2 -6x-6x +9
Combine like terms
4x^2 -12x +9
The area is 4x^2 -12x +9 ft^2
9514 1404 393
Answer:
1. ∠EDF = 104°
2. arc FG = 201°
3. ∠T = 60°
Step-by-step explanation:
There are a couple of angle relationships that are applicable to these problems.
- the angle where chords meet is half the sum of the measures of the intercepted arcs
- the angle where secants meet is half the difference of the measures of the intercepted arcs
The first of these applies to the first two problems.
1. ∠EDF = 1/2(arc EF + arc UG)
∠EDF = 1/2(147° +61°) = 1/2(208°)
∠EDF = 104°
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2. ∠FHG = 1/2(arc FG + arc ES)
128° = 1/2(arc FG +55°) . . . substitute given information
256° = arc FG +55° . . . . . . multiply by 2
201° = arc FG . . . . . . . . . subtract 55°
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3. For the purpose of this problem, a tangent is a special case of a secant in which both intersection points with the circle are the same point. The relation for secants still applies.
∠T = 1/2(arc FS -arc US)
∠T = 1/2(170° -50°) = 1/2(120°)
∠T = 60°
