If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases - Maths - Some Applications of Trigonometry

Question

If the shadow of a building increases by 10 meters when the
angle of elevation of the sun rays decreases from 70o to
60o, what is the height of the building?

Lovina Kansal · Accepted Answer

Dear student
Let AB be the building
 Let its height be h m
CD=10m (given)Let BC=x mIn △ABC,tan70°=ABBCtan70°=hx    h=xtan70°        
(1)In△ABD,tan60°=ABBDtan60°=hx+10h=tan60°x+10xtan70°=tan60°x+10     (from 1)x(tan70°-tan60°)=10 tan60°x=10 tan60°tan70°-tan60°Put in eq(1), we geth=10 tan60°tan70°-tan60°×tan70°h=46
86 (approx)
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If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70o to 60o, what is the height of the building?

If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70^o to 60^o, what is the height of the building?