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A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 2, respectively. The angle between A and C is $\frac{5 π}{24}$ $(5pi)/24$ and the angle between B and C is $\frac{7 π}{24}$ $(7pi)/24$ . What is the area of the triangle?

1 Answer

Dec 9, 2015

Area $△ A B C = 7$ $triangle ABC = 7$

Explanation:

If $∠ (C : A) = \frac{5 π}{24}$ $/_(C:A) =(5pi)/24$
and
$∠ (B : C) = \frac{7 π}{24}$ $/_(B:C) = (7pi)/24$

then
$XXX ∠ (A : B) = π - (\frac{5 π}{24} + \frac{7 π}{24})$ $color(white)("XXX")/_(A:B) = pi - ((5pi)/24+(7pi)/24)$

$XXXXXXXX = π - \frac{12 π}{24} = \frac{π}{2}$ $color(white)("XXXXXXXX")=pi-(12pi)/24 = pi/2$

i.e. $∠ (A : B)$ $/_(A:B)$ is a right angle
enter image source here

Treating $A$ $A$ as the base and $B$ $B$ as the height:

$XXX A r e a = \frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times 7 \times 2 = 7$ $color(white)("XXX")Area = 1/2xxbasexxheight = 1/2xx7xx2 = 7$

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