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Question
A tent is a shape of a triangular 'prism' resting on a rectangular side PQ = PR, PT = 1.5 m, QR = 1.8 m, length of the tent = 3 m. Find:
- ∠PQR
- The volume of the tent
Solution
Given: QR = 1.8 m, PT = 1.5 m, PQ = PR.
Since, PQ = PR
So, ΔPQR is an isosceles triangle.
So, PT bisects QR.
∴ QT = `1.8/2` = 0.9
i. tan Q = `"Perpendicular"/"Base"`
tan Q = `(1.5)/(0.9)`
tan Q = 1.6666666667
⇒ Q = 59.036°
Hence, ∠PQR = 59.036°.
ii. Volume of the tent,
V = `1/2` LWH
Here, L = 3 m, W = 1.8 m and H = 1.5 m
∴ V = `1/2 xx 3 xx 1.8 xx 1.5` = 4.05 m3
As a result, the volume of the tent is 4.05 m3.
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