Answer:
1) Option B is correct.
Cos b = four fifths
2) Option D is correct.
z = 6°
3) Option C is correct.
3 over 3 and 61 hundredths = 6 over 7 and 22 hundredths
Step-by-step explanation:
1) In triangle JKL,
Tan b = three fourths = (3/4)
Sin b = three fifths = (3/5)
Triangle JKL is then dilated by a scale factor of 3. What is cos b?
Note that dilating a structure by whatever scale factor only affects the lengths of the sides of the Triangle, the angles of the Triangle remain the same.
Tan b remains = (3/4)
Sin b remains = (3/5)
And from trigonometric relations
(Sin b)/(cos b) = tan b
Cos b = (Sin b)/(tan b)
Cos b = (3/5) ÷ (3/4)
Cos b = (3/5) × (4/3) = (4/5)
Cos b = four fifths.
2) sin(9z − 1) = cos(6z + 1) in the range 0 < z ≤ 90
Note that cosine and some are related through cos θ = sin (90 - θ)
So, cos (6z + 1) = Sin [90 - (6z + 1)] = Sin (90 - 6z - 1)
sin(9z − 1) = cos(6z + 1)
Sin (9z - 1) = Sin (90 - 6z - 1)
We can then equate the angles
9z - 1 = 90 - 6z - 1
9z + 6z = 90°
15z = 90°
z = 6°
3) Triangle BDE is dilated by a scale factor of 2 to obtain triangle BAC.
Dilation by a scale factor of 2 means that all the sides of triangle BAC are twice as much as the corresponding sides of triangle BDE.
And triangle BDE is similar to triangle BAC.
It also means that the corresponding angles are necessarily equal.
BD = 2
BE = 3
ED = 3.61
BA = 2 × BD = 2 × 2 = 4
BC = 2 × BE = 2 × 3 = 6
CA = 2 × ED = 2 × 3.61 = 7.22
Cos ∠D according to trigonometric relations is given as (adj/hyp)
Adj = Adjacent side = BE = 3
Hyp = hypotenuse side = ED = 3.61
Cos ∠D = (3/3.61)
Cos ∠A can also be similarly obtained from trigonometric relations as (adj/hyp)
Adj = Adjacent side = BC = 6
Hyp = hypotenuse side = CA = 7.22
Cos ∠A = (6/7.22)
Since the two angles are corresponding angles of two similar triangles,
We can easily see that
Cos ∠D = Cos ∠A
(3/3.61) = (6/7.22) = 0.8310
Which is necessarily equal to each other
Hence, the proportion that proves that Cos ∠D = Cos ∠A is 3 over 3 and 61 hundredths = 6 over 7 and 22 hundredths.
Hope this Helps!!!
