In the given figure is -5- - If -3-2 then x isA- 212 cmB- 252 cmC- 174 cmD- 56 cm

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Finding Unknown Angles

In the given ...

Question

In the given figure h = 11 cm and angle of prism is $θ = 5^{\circ}$ . If $μ = \frac{3}{2}$ then $x$ is

212 cm

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252 cm

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174 cm

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56 cm

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Solution

The correct option is B 252 cm

For small angle prism,

$δ = (μ - 1) A$

Since $A$ and $δ$ are very small, we can say

$\Rightarrow t a n δ = δ = \frac{h}{x} \Rightarrow \frac{h}{x} = (μ - 1) A$

$x = \frac{h}{(μ - 1) A} = \frac{11}{(\frac{3}{2} - 1) 5 \times \frac{π}{180}} = \frac{11 \times 2 \times 180 \times 7}{5 \times 22} = 252 c m$

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In the given figure h = 11 cm and angle of prism is θ=5∘. If μ=32 then x is

The correct option is B 252 cm For small angle prism, δ=(μ−1)A Since A and δ are very small, we can say ⇒tan δ=δ=hx⇒hx=(μ−1)A x=h(μ−1)A=11(32−1)5×π180=11×2×180×75×22=252 cm

In the given figure h = 11 cm and angle of prism is $θ = 5^{\circ}$ . If $μ = \frac{3}{2}$ then $x$ is