Answer:


Step-by-step explanation:
To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.
a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

we can substitute the value of sec(θ) in this equation:

and solve for for cos(θ)

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by
b) since right triangle is mentioned in the question. We can use:

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:
- length of the adjacent side = 1
- length of the hypotenuse = 52
we can find the third side using the Pythagoras theorem.




- length of the opposite side = √(2703) ≈ 51.9904
we can find the sin(θ) using this side:


and since 

Answer:
150.08 inches
Step-by-step explanation:
The question simply requires that we find the length of the arc that the dog walks.
Its leash rotates through 150° and the length of the leash (radius) is 60 inches.
The length of an arc is given as:
L = α/360 * 2πR
where α = angle of arc
R =radius
Therefore:
L = 150/360 * 2 * π * 60
L = 150.08 inches
The dog walks 150.08 inches
Answer:
1:3
Step-by-step explanation:
The required ratio will be ,
7:21
= 1 :3
The line passes through (2,-3) and (4,2).
Calculate the slope of the line.
m = (2+3)/(4-2) = 5/2
The equation of the line is therefore

Cross multiply.
2(y-2) = 5(x-4)
2y - 4 = 5x - 20
2y = 5x - 16
Rewrite as
5x - 2y = 16
Answer: C. 5x - 2y = 16
Given that AB has been dilated by scale factor 3 to form A'B', and by laws of dilation, the image is congruent to the pre image. This implies that the image will not change in any way whatsoever apart from the size. Hence the slope will remain the same. That means the slope of A'B' will be 3