Question

23. The angles of a triangle are in ratio \( 2: 3 \) and the third is \( \frac{4 \pi^{c}}{9} \). Find the all angles in degrees.

Ask by Coles Floyd. in Nepal
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The angles of the triangle are 40°, 60°, and 80°.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

The Deep Dive

To solve for the angles of the triangle, let's denote the angles as \( 2x \), \( 3x \), and the third angle \( \frac{4\pi^c}{9} \). We know that the sum of the angles in a triangle is \( 180^\circ \). First, we convert \( \frac{4\pi^c}{9} \) from radians to degrees. Since \( \pi \) radians is equal to \( 180^\circ \), we can find the equivalent degree measure: \[ \frac{4\pi^c}{9} \text{ radians} = \frac{4\pi^c \times 180^\circ}{\pi} = \frac{720^c}{9} = 80^c. \] Now, we can set up the equation for the sum of angles: \[ 2x + 3x + 80^c = 180^\circ. \] Combining the terms gives: \[ 5x + 80^c = 180^\circ. \] From this, we can isolate \( 5x \): \[ 5x = 180^\circ - 80^c. \] Next, we can find the measure of \( x \): \[ x = \frac{180^\circ - 80^c}{5}. \] Now we can substitute \( x \) back into the expressions for the angles: 1. First angle: \( 2x = 2 \left( \frac{180^\circ - 80^c}{5} \right) = \frac{360^\circ - 160^c}{5} \). 2. Second angle: \( 3x = 3 \left( \frac{180^\circ - 80^c}{5} \right) = \frac{540^\circ - 240^c}{5} \). 3. The third angle: \( 80^c \). Thus, the angles of the triangle are: - Angle 1: \( \frac{360 - 160^c}{5} \) degrees. - Angle 2: \( \frac{540 - 240^c}{5} \) degrees. - Angle 3: \( 80^c \) degrees. This gives a complete set of angles for the triangle based on the provided ratios and third angle.

Latest Geometry Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy