Question
Download Solution PDF\(\triangle\)ABC is a right-angle triangle at B and tan A = \(\frac{3}{4}\), then sin A + sin B + sin C will be equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
ΔABC is a right-angle triangle at B and tan A = \(\frac{3}{4}\)
Concept used:
1. tan θ = Height ÷ Base
2. sin θ = Height ÷ Hypotenuse
3. Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Calculation:
tan A = \(\frac{3}{4}\)
⇒ \(\frac {BC}{AB}\) = \(\frac{3}{4}\)
⇒ BC : AB = 3 : 4
Let the measure of BC and AB be 3k and 4k respectively.
According to the concept,
AC2 = \(\sqrt { (3k)^2 + (4k)^2 }\) = 5k
Now, sin A + sin B + sin C
⇒ \(\frac {BC}{AC} + sin\ 90^\circ + \frac {AB}{AC}\)
⇒ \(\frac {BC + AB}{AC} + 1\)
⇒ \(\frac {3k + 4k}{5k} + 1\)
⇒ \(\frac {7}{5} + 1\)
⇒ \(\frac {12}{5}\) = \(2\frac{2}{5}\)
∴ The value of sin A + sin B + sin C is \(2\frac{2}{5}\).
Last updated on Jul 9, 2025
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