To determine which of the given angles is not a measure of one of the interior angles of the given right triangle, ASMA, we need to follow these steps:
1. Understand the Triangle:
- The triangle ASMA is described as a 3-4-5 right triangle.
- Therefore, it has sides of lengths 3, 4, and 5 units.
- The right triangle assures that one of its angles is 90°.
2. Identify the Angles:
- Let's denote the angles as [tex]\( \angle A \)[/tex], [tex]\( \angle B \)[/tex], and [tex]\( \angle C \)[/tex], where [tex]\( \angle C \)[/tex] is the right angle (90°).
3. Use Trigonometric Ratios:
- For right triangles, we can use trigonometric ratios to find the remaining angles.
4. Calculate [tex]\( \angle A \)[/tex] and [tex]\( \angle B \)[/tex]:
- Recall that:
- [tex]\( \tan(\theta) = \text{opposite} / \text{adjacent} \)[/tex]
- Using trigonometric ratios:
- [tex]\( \angle A \)[/tex] (adjacent side is 4, opposite side is 3):
[tex]\[
\tan^{-1}\left(\frac{3}{4}\right)
\][/tex]
- [tex]\( \angle B \)[/tex] (adjacent side is 3, opposite side is 4):
[tex]\[
\tan^{-1}\left(\frac{4}{3}\right)
\][/tex]
5. Convert to Degrees:
- The values of these angles need to be calculated in degrees.
- Typically in a 3-4-5 triangle:
- [tex]\( \angle A \approx 36.87^\circ \)[/tex]
- [tex]\( \angle B \approx 53.13^\circ \)[/tex]
- Remembering LAM rule that the sum of angles in any triangle is [tex]\( 180^\circ \)[/tex], we have:
[tex]\[
\angle A + \angle B + \angle C = 180^\circ
\][/tex]
6. List the Possible Measures:
- The measures of the interior angles of this triangle are 36.87°, 53.13°, and 90.00°.
7. Identify the Outlier:
- Comparing these to the given options: 29.54°, 36.87°, 53.13°, and 90.00°, it is apparent that 29.54° does not match any of the measures of the computed angles.
Hence, the measure that is not an interior angle of the given right triangle ASMA is:
```
29.54°
```
