Math  /  Trigonometry

QuestionDetermine the number of triangles ABCA B C possible with the given parts. A=40.1a=8.5b=10.4A=40.1^{\circ} \quad a=8.5 \quad b=10.4
How many possible solutions does this triangle have? \square

Studdy Solution
Determine the number of possible triangles based on sinB\sin B:
1. Check if sinB1\sin B \leq 1. Since sinB0.786\sin B \approx 0.786, it is valid.
2. Calculate the angle B B using sin1(0.786)\sin^{-1}(0.786).

Bsin1(0.786)51.8 B \approx \sin^{-1}(0.786) \approx 51.8^\circ
3. Check for the possibility of a second triangle using the supplementary angle:
B=18051.8=128.2 B' = 180^\circ - 51.8^\circ = 128.2^\circ
4. Verify if A+B<180 A + B' < 180^\circ :
40.1+128.2=168.3 40.1^\circ + 128.2^\circ = 168.3^\circ
Since 168.3<180 168.3^\circ < 180^\circ , both B B and B B' are valid.
Thus, there are 2 possible triangles.
The number of possible solutions for the triangle is:
2 \boxed{2}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord