Can someone help me on this please

∠B = 68.20°

Step-by-step explanation:

Since this is a right triangle, we can use the trigonometry ratios to solve. Remember them using the acronym "SohCahToa".

sinθ = opposite/hypotenuse

cosθ = adjacent/hypotenuse

tanθ = opposite/adjacent

θ means the angle of reference, or angle you are talking about.

Hypotenuse is the longest side. Adjacent side touches θ and is not the hypotenuse. The opposite side does not touch θ.

In this problem, θ = ∠B.

The side we know are AC = 5 and BC = 2.

To ∠B, BC is adjacent. AC is opposite.

The trig. ratio with opposite and adjacent is:

tanθ = opposite/adjacent

Use this ratio formula and solve for ∠B.

tanθ = opposite/adjacent

tanB = AC/BC                   Insert variables from the diagram

tanB = 5/2                     Substitute known values

B = tan⁻¹(5/2)                    Isolate "B"

B = tan⁻¹(2.5)                    Simplified fraction

B = 68.19859051°             Unrounded answer on your calculator

B ≈ 68.20°                 Rounded to the nearest hundredth

How to round:

Focus on one more digit than you are rounding to:

Hundredth is the 2nd decimal digit. One over to the right is the third:

68.198 5905

The third decimal digit determines if you round up or down.

Round up if: 5 or greater

Round down if: 4 or less

8 is 5 or greater, so round up by increasing the hundredth digit by one. Drop the third decimal digit.

68.19

+0.01

68.20

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.