Question
Use the inverse of cosine to find the approximate measure of the missing angle θ . (1 point) Responses 43° 43° 90° 90° 30.5° 30.5° 59.5° (The angles are 56, 33, and 65. We also have a 90 degree angle)
Answers
Answered by
GPT-4o mini
To find the missing angle \( \theta \) in a right triangle, you can use the fact that the sum of angles in a triangle is \( 180^\circ \). In a right triangle, one of the angles is \( 90^\circ \).
Given angles are:
- \( 56^\circ \)
- \( 33^\circ \)
- \( 65^\circ \)
- \( 90^\circ \) (right angle)
Since there is a right angle (\( 90^\circ \)), we need to find the missing angle that completes the triangle's angle sum.
Let's first assume:
\[ \theta + 56^\circ + 90^\circ = 180^\circ \]
We can solve for \( \theta \):
\[ \theta = 180^\circ - 90^\circ - 56^\circ \]
\[ \theta = 34^\circ \]
However, none of the provided options directly match this angle. So let's check if \( \theta \) might be one of the angles given the other two angles:
1. If the angles are \( 33^\circ \) and \( 65^\circ \), let's check:
\[ \theta + 33^\circ + 65^\circ = 180^\circ \]
Here, we find \( \theta \):
\[ \theta = 180^\circ - 33^\circ - 65^\circ \]
\[ \theta = 180^\circ - 98^\circ \]
\[ \theta = 82^\circ \] (not an option)
2. Now let’s check the configuration:
If we want to find a corresponding angle for either of the given seats using cosine inverse, for missing angle \( \theta \):
None of the given options directly relate.
However, we can arrive at the answer by finalizing our check again thoroughly.
Given:
- Shown angles one of which is \( 90^\circ \).
Let's summarize possible angles:
Using triangle angle formulas,
- The angles given (56 and 33), completing the directly implied value is:
- \[ 90 - 56 = 34^\circ \]
- \[ 90 - 33 = 57^\circ \] therefore options may not yield directly
The options could allow \( 43^\circ \).
Since the answered \( \theta \) is calculated with reliance on context,
The closest option to the unknown calculated angle will be \( 43^\circ \) in aligning context.
Final conclusion:
The response needed from options seems to yield closest \( \theta \) as **43°**.
Given angles are:
- \( 56^\circ \)
- \( 33^\circ \)
- \( 65^\circ \)
- \( 90^\circ \) (right angle)
Since there is a right angle (\( 90^\circ \)), we need to find the missing angle that completes the triangle's angle sum.
Let's first assume:
\[ \theta + 56^\circ + 90^\circ = 180^\circ \]
We can solve for \( \theta \):
\[ \theta = 180^\circ - 90^\circ - 56^\circ \]
\[ \theta = 34^\circ \]
However, none of the provided options directly match this angle. So let's check if \( \theta \) might be one of the angles given the other two angles:
1. If the angles are \( 33^\circ \) and \( 65^\circ \), let's check:
\[ \theta + 33^\circ + 65^\circ = 180^\circ \]
Here, we find \( \theta \):
\[ \theta = 180^\circ - 33^\circ - 65^\circ \]
\[ \theta = 180^\circ - 98^\circ \]
\[ \theta = 82^\circ \] (not an option)
2. Now let’s check the configuration:
If we want to find a corresponding angle for either of the given seats using cosine inverse, for missing angle \( \theta \):
None of the given options directly relate.
However, we can arrive at the answer by finalizing our check again thoroughly.
Given:
- Shown angles one of which is \( 90^\circ \).
Let's summarize possible angles:
Using triangle angle formulas,
- The angles given (56 and 33), completing the directly implied value is:
- \[ 90 - 56 = 34^\circ \]
- \[ 90 - 33 = 57^\circ \] therefore options may not yield directly
The options could allow \( 43^\circ \).
Since the answered \( \theta \) is calculated with reliance on context,
The closest option to the unknown calculated angle will be \( 43^\circ \) in aligning context.
Final conclusion:
The response needed from options seems to yield closest \( \theta \) as **43°**.