Question

the angle of elevation of the top of a tower from a point a due soaked of Tower is alpha and from be due east of Tower is better if a b is equals to de show that the height of the tower is the divided by root cos square alpha + cos square beta​

Answer 1

Answer:

Let OP be the tower and let A and B be two points due south and east

respectively of the tower such that

∠OAP=α

and ∠OBP=β.

Let OP=h

InΔOAP,wehave

tanα=

OA

h

OA=hcotα..............(i)

InΔOBP,wehave

tanβ=

OB

h

OB=hcotβ..............(i)

Since OAB is a right angled triangle .

Therefore ,

AB

2

=OA

2

+OB

2

d

2

=h

2

+cot

2

α+h

2

+cot

2

β

∴h=

cot

2

α+cot

2

β

d

[using(i)and(ii)]

solution

Step-by-step explanation:

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Answer 2

Answer:

ANSWER

Let OP be the tower and let A and B be two points due south and east

respectively of the tower such that

∠OAP=α

and ∠OBP=β.

Let OP=h

InΔOAP,wehave

tanα=

OA

h

OA=hcotα..............(i)

InΔOBP,wehave

tanβ=

OB

h

OB=hcotβ..............(i)

Since OAB is a right angled triangle .

Therefore ,

AB

2

=OA

2

+OB

2

d

2

=h

2

+cot

2

α+h

2

+cot

2

β

∴h=

cot

2

α+cot

2

β

d

[using(i)and(ii)]

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