A boy saw the top of a building under construction at an elevation of $3 0^{o}$ . The completed building was $12 m$ higher and the boy saw its top at an elevation of $6 0^{o}$ from the same spot.
a. Draw a rough figure based on the given details.
b. What is the height of the building?
c. What is the distance between the building and the boy?

Question

A boy saw the top of a building under construction at an elevation of

3 0^{o}

. The completed building was

12 m

higher and the boy saw its top at an elevation of

6 0^{o}

from the same spot.
a. Draw a rough figure based on the given details.
b. What is the height of the building?
c. What is the distance between the building and the boy?

Filo · Accepted Answer

a. ref. imageb. Consider AC=x,AD=x+12In triangle ABD, ABAD​=tan60oAB=tan60oAD​⇒AB=3​x+12​   ...(1)In triangle ABC,ABAC​tan30o⇒AB=3​1​=x3​...(2)Comparing equation (1) and (2)ie., 3​x+12​=x3​⇒3x=x+12⇒3x−x=12,⇒2x=12,x=6Hence, the height of the building =6+12=18m.c. Consider the equation (2)ie. AB=3​x=3​×6=1.73×6=10.38mDistance between the building and the boy =10.38m

Question Text	A boy saw the top of a building under construction at an elevation of $3 0^{o}$ . The completed building was $12 m$ higher and the boy saw its top at an elevation of $6 0^{o}$ from the same spot. a. Draw a rough figure based on the given details. b. What is the height of the building? c. What is the distance between the building and the boy?
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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