Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

13. (a) If two angles of a triangle are [tex]45^{\circ}[/tex] and [tex]\left(\frac{\pi}{6}\right)^{\circ}[/tex], find the remaining angle in degrees.

Sagot :

To find the remaining angle of a triangle when two angles are given, we need to recall that the sum of all interior angles in any triangle is always [tex]\(180^\circ\)[/tex]. Given the two known angles, we can follow these steps:

1. Convert the angle given in radians to degrees:

The given angle is [tex]\(\left(\frac{\pi}{6}\right)^{\circ}\)[/tex].

Knowing the conversion factor [tex]\(1 \text{ radian} = 180^\circ / \pi\)[/tex], we convert [tex]\(\frac{\pi}{6}\)[/tex] radians to degrees as follows:
[tex]\[ \left(\frac{\pi}{6}\right) \times \left(\frac{180^\circ}{\pi}\right) = 30^\circ \][/tex]

So, [tex]\(\frac{\pi}{6}\)[/tex] radians is equivalent to [tex]\(30^\circ\)[/tex].

2. Identify the known angles in degrees:

The two given angles are:
[tex]\[ 45^\circ \quad \text{and} \quad 30^\circ \][/tex]

3. Calculate the remaining angle:

Using the fact that the sum of the angles in a triangle is [tex]\(180^\circ\)[/tex], we find the remaining angle by subtracting the sum of the known angles from [tex]\(180^\circ\)[/tex]:
[tex]\[ \text{Remaining angle} = 180^\circ - (45^\circ + 30^\circ) \][/tex]
[tex]\[ \text{Remaining angle} = 180^\circ - 75^\circ = 105^\circ \][/tex]

Thus, the remaining angle in the triangle is:
[tex]\[ 105^\circ \][/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.