Question

In a triangle ABC with usual notations if \(\mathrm{a}=13\), \(b=14, c=15\) Then \(\sin A=\)

• A. \(\frac{4}{5}\)
• B. \(\frac{3}{5}\)
• C. \(\frac{1}{2}\)
• D. \(\frac{4}{7}\)

Hint:

Find the area with Heron's formula and use area = (1/2) b c sin A.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Heron's formula gives the area, and \(\Delta=\frac12bc\sin A\) then gives \(\sin A\).

Step 2: Find the area
\(s=\frac{13+14+15}{2}=21\)
\(\Delta=\sqrt{21\cdot8\cdot7\cdot6}=84\).

Step 3: Find sin A
\(\sin A=\frac{2\Delta}{bc}=\frac{168}{14\cdot15}=\frac{168}{210}=\frac45\).

Final Answer:
\(\sin A=\frac45\). \[ \boxed{\text{(A) }\dfrac{4}{5}} \]