Question

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10. [5 Points) A triangular truss is shown in the figure below. Find angle 8. 16 ft 13 ft

Answer 1

Solution-

Let us mark the corners of triangular truss as A, B and C & their corrosponding sides as a, b and c respectively.

As shown in figure below-

C 2013 b-16/1 A 02201

Now,

We have a = 13 ft , b =16 ft and c = 20 ft and A =$\theta$

So, s = (a+b+c)/2 =(13+16+20)/2 =49/2=24.5

We know that

COS s(s – a) bc 2

On putting the A= $\theta$ , s =24.5, a =13 ft, b =16 ft and c =20 ft, we get

COS 24.5(24.5 – 13) (16) (20)

$cos\left ( \frac{\theta}{2} \right )=\sqrt{\frac{24.5(11.5)}{320}}$

$cos\left ( \frac{\theta}{2} \right )=\sqrt{\frac{281.75}{320}}$

$cos\left ( \frac{\theta}{2} \right )=\sqrt{0.88046875}$

$cos\left ( \frac{\theta}{2} \right )=0.938333$

$\frac{\theta}{2} =cos^{-1}(0.938333)$

$\frac{\theta}{2} =20.22654217^o$

$\theta=2*20.22654217^o$

$\theta=40.45^o$

Hence, $\theta=40.45^o$