Question
USE THE COS METHOD Solve for xx. Round to the nearest tenth of a degree, if necessary.
O
P
Q
77
67
x°
Answer
Attempt 1 out of 2
x, equalsx=
degrees
∘
O
P
Q
77
67
x°
Answer
Attempt 1 out of 2
x, equalsx=
degrees
∘
Answers
GPT-4o mini
To solve for \( x \) using the cosine (cos) method in the context of a triangle, we generally apply the Law of Cosines, which states:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
where \( C \) is the angle opposite side \( c \), and \( a \) and \( b \) are the lengths of the other two sides.
From your information, we have two angles \( P \) and \( Q \), which are \( 77^\circ \) and \( 67^\circ \) respectively. We can find the third angle \( x \) using the fact that the sum of the angles in a triangle is \( 180^\circ \):
\[
x = 180^\circ - P - Q
\]
Substituting in the values:
\[
x = 180^\circ - 77^\circ - 67^\circ
\]
\[
x = 180^\circ - 144^\circ
\]
\[
x = 36^\circ
\]
Thus, the value of \( x \) is:
\[
\boxed{36^\circ}
\]
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
where \( C \) is the angle opposite side \( c \), and \( a \) and \( b \) are the lengths of the other two sides.
From your information, we have two angles \( P \) and \( Q \), which are \( 77^\circ \) and \( 67^\circ \) respectively. We can find the third angle \( x \) using the fact that the sum of the angles in a triangle is \( 180^\circ \):
\[
x = 180^\circ - P - Q
\]
Substituting in the values:
\[
x = 180^\circ - 77^\circ - 67^\circ
\]
\[
x = 180^\circ - 144^\circ
\]
\[
x = 36^\circ
\]
Thus, the value of \( x \) is:
\[
\boxed{36^\circ}
\]