Question

A tent is in the shape of triangular prism resting on arectangular base.If AB=CD,AD=0.8m,BC=3m and a lebgth of the tent=6m Angle ABC=42 degree then fin{Refer the image}

Answer 1

from ∆ABC,
$\angle{ACB}=\angle{ABC}$ [because AB = AC ]

so, $\angle{ACB}=42^{\circ}$

see triangle , ∆ABD
$sin\angle{ACB}=\frac{AD}{AB}$

or, sin42° = 0.8/AB

or, AB = 0.8/sin42° = 1.196 m ≈ 1.2 m

now, volume of tent = area of ∆ABC × length of tent

= 1/2 × AD × BC × length of tent

given, length of tent = 6m
BC = 3m , AD = 0.8m

so, volume of tent = 1/2 × 0.8 × 3 × 6

= 0.4 × 18 = 7.2 m³