Answer:
∠B = 68.20°
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