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3 votes
In ΔABC, the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively.

m∠B =
º, and m∠C =
º.

Round off your answers to two decimal places.

User Ugh
by
7.7k points

1 Answer

4 votes

Explanation:

I assume that b is the opposite side of angle B, and c is the opposite side of angle C.

so,

a = 22.5 cm

b = 18 cm

c = 13.6 cm

remember the law of cosine :

c² = a² + b² - 2ab×cos(C)

c is the side opposite of the angle C, a and b are the other 2 sides.

that works for any angle and/or side of every triangle. you only need to set c as the side opposite of a specific angle (which you set to be C), and the other 2 sides are a and b.

contrary to Pythagoras for right-angled triangles, c does not have to be a baseline or longest side.

so, I keep here the original side and angle names to make it clearer. to get angle B :

b² = a² + c² - 2ac×cos(B)

2ac×cos(B) = a² + c² - b²

cos(B) = (a²+c²-b²)/(2ac) = (22.5²+13.6²-18²)/(2×22.5×13.6) =

= (506.25+184.96-324)/612 = 367.21/612 =

= 0.60001634...

angle B = 53.12893209...° ≈ 53.13°

to get angle C :

c² = a² + b² - 2ab×cos(C)

2ab×cos(C) = a² + b² - c²

cos(C) = (a²+b²-c²)/(2ab) = (22.5²+18²-13.6²)/(2×22.5×18) =

= (506.25+324-184.96)/810 = 645.29/810 =

= 0.796654321...

angle C = 37.18820916...° ≈ 37.19°

User Yafa
by
7.7k points