Question

The shadow of the pole is 5m long when the angle elevation of the sun is 60. Find the length of the shadow when the angle of elevation of the sun is 45

Answer 1

Answer:

tan 60=x/5

tan 45 =x/y

y=tan45/x

=> y= tan45/5tan60

=> y =1/5×3^1/2

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Length\:of\:shadow=}5\sqrt{3}\:m}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about The shadow of the pole is 5m long when the angle elevation of the sun is 60.

• We have to find the length of the shadow when the angle of elevation of the sun is 45.

$\green{\underline \bold{Given :}} \\ : \implies \text{Angle\:of\:elevation\:first=}60^{\circ}\\\\ :\implies \text{Shadow\:of\:pole=5\:m}\\\\ : \implies \text{Angle\:of\:elevation\:second=}45^{\circ}\\ \\ :\implies \text{Shadow\:of\:pole=5\:m} \\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Length\:of\:shadow= ?}$

• Accroding to given question :

$\bold{In \: \triangle \: ABC} \\ : \implies tan \: \theta = \frac{\text{Perpendicular}}{\text{Base}} \\ \\ : \implies tan \: 60^{\circ}= \frac{AB}{BC} \\ \\ : \implies \sqrt{3} = \frac{AB}{5} \\ \\ \green{ : \implies AB=5\sqrt{3}\:m}$

$\bold{In \: \triangle \: ABD} \\ : \implies tan \theta = \frac{p}{b} \\ \\ : \implies tan \: 45 ^{ \circ} = \frac{AB}{BD} \\ \\ : \implies 1 = \frac{5 \sqrt{3} }{BD} \\ \\ \green{\implies \text{BD= 5 }\sqrt{3} m}$