Answer :
The measure of ∠F of the triangle FGH, where all the sides are known is 74 degrees to the nearest degree.
What is the law of cosine?
When the three sides of a triangle is known, then to find any angle, the law of cosine is used.
It can be given as,
[tex]c^2=a^2+b^2-2ab\cos C\\a^2=c^2+b^2-2ab\cos A\\b^2=a^2+c^2-2ab\cos B[/tex]
Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.
In the triangle FGH the measure of the line segment f is 60 centimeter, the measure of the line segment g is 10 cm and the measure of the line segment h is 62 centimeters.
The measure of the angle ∠F has to be find out. To find the value of angle F where side f is 60 cm. Thus, put the values of the all the sides in the above formula as,
[tex]60^2=10^2+62^2-2(10)(62)\cos (F)\\3600=100+3844-1240\cos (F)\\ F=\cos^{-1}(0.27742)\\F\cong74^o[/tex]
Hence, the measure of ∠F of the triangle FGH, where all the sides are known is 74 degrees to the nearest degree.
Learn more about the law of cosine here;
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