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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