Review the diagram.

On a coordinate plane, a vector labeled 120 meters forms angle 25 degrees with the x-axis. It goes to point mirror 1. Another vector labeled 90 meters goes from point mirror 1 to mirror 2. It forms angle 20 degrees with a horizontal line. Point mirror 2 goes to (0, 0).

A laser beam is aimed 25° from horizontal at a mirror 120 m away. The beam bounces off the mirror and continues for an additional 90 m at 20° above horizontal until it hits a target, mirror 2. What is the distance between the origination point and the target?

approximately 85 m
approximately 122 m
approximately 174 m
approximately 194 m

Approximately 85 m

Step-by-step explanation:

Let x represent the distance between the origination point and the target

Distance between original point and mirror 1 = 120 m

Distance between mirror 1 and mirror 2 = 90 m

The measure of angle Opposite the distance between the origination point and the target = 20 + 25 = 45°

Use Cosine rule to find x as shown below:

Use The Law of Cosines to find side a first:

Where,

a = x

b = 90 m

c = 120 m

A = 45°

Plug in the values

Square both sides

x ≈ 85 m

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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