A hall has a square floor of dimension 10 m × 10 m (see the figure) and vertical walls. If the angle GPH between the diagonals A G and B H is cos -1 (1/5), then the height of the hall (in meters) is :

Question

A hall has a square floor of dimension 10 m × 10 m (see the figure) and vertical walls. If the angle GPH between the diagonals A G and B H is cos -1 (1/5), then the height of the hall (in meters) is : (A)  5 (B) 2 √10 (C) 5 √3 (D) 5 √2

Tardigrade Admin · Accepted Answer

A ( hat j ) ⋅ B (10 hat i ) H ( hat h hat j +10 hat k ) G (10 hat i + h hat j +10 hat k ) AG =10 hat i + hj +10 hat k BH =-10 hat i + h hat j +10 hat k cos θ=( AG BH /| AG || BH |) (1/5)=( h 2/ h 2+200) 4 h2=200 ⇒ h=5 √2

Q. A hall has a square floor of dimension $10 m \times 10 m$ (see the figure) and vertical walls. If the angle GPH between the diagonals $A G$ and $B H$ is $cos^{- 1} \frac{1}{5}$ , then the height of the hall (in meters) is :

$5$

$210$

$53$

$52$

Q. A hall has a square floor of dimension 10m×10m (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is cos−151​, then the height of the hall (in meters) is :

5

210​

53​

52​

A(j^​)⋅B(10i^) H(h^j^​+10k^) G(10i^+hj^​+10k^) AG=10i^+hj+10k^ BH=−10i^+hj^​+10k^ cosθ=∣AG∣∣BH∣AGBH​ 51​=h2+200h2​ 4h2=200 ⇒h=52​

Q. A hall has a square floor of dimension $10 m \times 10 m$ (see the figure) and vertical walls. If the angle GPH between the diagonals $A G$ and $B H$ is $cos^{- 1} \frac{1}{5}$ , then the height of the hall (in meters) is :

$5$

$210$

$53$

$52$