Question

Find m Write answer as an integer or as a decimal rounded to the nearest tenth

Answer 1

The answer is 66.4

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Step-by-step explanation:

We have a right triangle because the square marker (angle C) indicates a right 90 degree angle. Therefore we can use a trig function to help find the measure of angle B.

With angle B as the reference angle, we see that segment BC = 4 is the adjacent side and segment AB = 10 is the hypotenuse. The ratio of the adjacent and hypotenuse is equal to the cosine of the reference angle

cos(angle) = adjacent/hypotenuse

cos(B) = BC/AB

cos(B) = 4/10

cos(B) = 0.4

Now use the inverse cosine or arccosine function to undo the cosine function on the left side. This will isolate B

cos(B) = 0.4

arccos(cos(B)) = arccos(0.4)

B = arccos(0.4)

B = 66.4218215217981 see note below

B = 66.4

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note: you will need your calculator for this step. Make sure your calculator is in degree mode. On many calculators, the inverse cosine button is marked as "cos" with a "-1" as an exponent. The result shown is approximate.

Answer 2

∠B = 66.4°

Step-by-step explanation:

Since the triangle is right use the cosine ratio to find ∠B

cosB =
`(adjacent)/(hypotenuse)` =
`(4)/(10)` =
`(2)/(5)`, thus

B =
`cos^(-1)`(
`(2)/(5)`) ≈ 66.4°