Question
Solve for xx. Round to the nearest tenth of a degree, if necessary. using the sin or cos and tan methods and tell me which ones is ths answer
M
N
O
20
43
x°
Answer
Attempt 1 out of 2
x, equalsx=
M
N
O
20
43
x°
Answer
Attempt 1 out of 2
x, equalsx=
Answers
GPT-4o mini
To solve for \( x \) in triangle \( MNO \) with the given angle measures, we need to clarify a few details about the triangle:
- Assign the known values: \( \angle M = 20^\circ \), \( \angle N = 43^\circ \), and we are solving for \( \angle O \) (which is \( x \)).
First, we can find the third angle in the triangle using the triangle sum theorem, which states that the sum of the angles in a triangle is \( 180^\circ \):
\[
x = 180^\circ - \angle M - \angle N
\]
Substituting in the known values:
\[
x = 180^\circ - 20^\circ - 43^\circ
\]
\[
x = 180^\circ - 63^\circ
\]
\[
x = 117^\circ
\]
Now, rounding to the nearest tenth of a degree (though not necessary here since it is already a whole number):
\[
x \approx 117.0^\circ
\]
Thus, the answer is \( x = 117^\circ \).
So you have:
- Using angle sum property (instead of sine, cosine, or tangent), we found the angle directly. The methods you mentioned (sin, cos, and tan) are typically used to find side lengths or angles in right triangles, but the angle sum property sufficed here.
- Assign the known values: \( \angle M = 20^\circ \), \( \angle N = 43^\circ \), and we are solving for \( \angle O \) (which is \( x \)).
First, we can find the third angle in the triangle using the triangle sum theorem, which states that the sum of the angles in a triangle is \( 180^\circ \):
\[
x = 180^\circ - \angle M - \angle N
\]
Substituting in the known values:
\[
x = 180^\circ - 20^\circ - 43^\circ
\]
\[
x = 180^\circ - 63^\circ
\]
\[
x = 117^\circ
\]
Now, rounding to the nearest tenth of a degree (though not necessary here since it is already a whole number):
\[
x \approx 117.0^\circ
\]
Thus, the answer is \( x = 117^\circ \).
So you have:
- Using angle sum property (instead of sine, cosine, or tangent), we found the angle directly. The methods you mentioned (sin, cos, and tan) are typically used to find side lengths or angles in right triangles, but the angle sum property sufficed here.