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Enter the number that belongs in the green box 7 4 8

Enter the number that belongs in the green box 7 4 8-example-1
User Zero Days
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1 Answer

3 votes

Answer:

61.03°

Explanation:

You want the angle opposite the side of length 7 in the triangle with other sides of lengths 4 and 8.

Law of Cosines

The law of cosines relates the angles of a triangle to the side lengths. For triangle ABC with opposite sides a, b, c, the relation is ...

c² = a² +b² -2ab·cos(C)

Application

Solving for angle C, we have ...

cos(C) = (a² +b² -c²)/(2ab)

C = arccos((a² +b² -c²)/(2ab))

In this triangle, that means ...

C = arccos((4² +8² -7²)/(2·4·8)) = arccos(31/64)

C ≈ 61.03°

The angle of interest is about 61.03°.

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Additional comment

We get the same result from a triangle solver. See the second attachment. (The angle we want is angle B in that attachment.)

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Enter the number that belongs in the green box 7 4 8-example-1
Enter the number that belongs in the green box 7 4 8-example-2
User Dewyze
by
8.3k points

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