Question

Can someone help me on this please

Answer 1

Explanation:

The triangle is a right angle triangle. Therefore, to find the hypotenuse side, |AB|;

AB^2 = AC^2 + CB^2

= sqrt(5^2 + 2^2)

= sqrt(29)

= 5.39

Using trigonometry equation,

Sin B = opp/hyp

B = arcsin(5/5.39)

= 68.20°

Answer 2

∠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