Respuesta :
Answer:
Let the height of building be h m.
Current angle of elevation is 30∘
Distance of observer from the base of building will be hcot(30∘) m = h3–√ m
Now the observer moves 30 m towards the base of building.
New distance of observer from the base of building will be = (h3–√−30) m
New angle of elevation is (30+15)∘=45∘
Distance of observer from the base of building will be hcot(45∘) m = h m
⇒h3–√−30=h
⇒h3–√−h=30
⇒h(3–√−1)=30
⇒h(3–√−1)=30
⇒h=303–√−1
⇒h=30(3–√+1)(3–√−1)(3–√+1)
⇒h=30(3–√+1)2
⇒h=15(3–√+1)
Height of the building is 15(3–√+1) m.
Step-by-step explanation:
Let the height of building be h m.
Current angle of elevation is 30∘
Distance of observer from the base of building will be hcot(30∘) m = h3–√ m
Now the observer moves 30 m towards the base of building.
New distance of observer from the base of building will be = (h3–√−30) m
New angle of elevation is (30+15)∘=45∘
Distance of observer from the base of building will be hcot(45∘) m = h m
⇒h3–√−30=h
⇒h3–√−h=30
⇒h(3–√−1)=30
⇒h(3–√−1)=30
⇒h=303–√−1
⇒h=30(3–√+1)(3–√−1)(3–√+1)
⇒h=30(3–√+1)2
⇒h=15(3–√+1)
Height of the building is 15(3–√+1) m.
