Math, asked by Caroline234, 10 months ago

Trigonometry 11.

1. is the angle of elevation of the top of the tower from two points at a distance of 4m and 9M from the base of the tower and in the same straight line with it are complementary find the height of the tower...

Answers

Answered by Anjula
47

Answer:

Step-by-step explanation:

Let the height of the tower ,AB be ‘h’

Let C be a point which is 4m away from the tower

I.e BC = 4m

Angle of elevation from point C be ‘x’

Angle C and Angle D are complementary angles .

So, Angle C + Angle D = 90°

Angle D = 90°-angle C

=> 90-x

D is a point 9m away from the tower I.e BD= 9m

In right triangle,ABC ,Angle B = 90°

AB =h ,BC=4m ,Angle ACB=x

Using Trigonometric ratios,

Tan C = AB/BC

Tan x = h/4—(1)

In right triangle ABD,Angle B = 90°

AB = h,BD=9m,Angle D = 90-x

Using Trigonometric ratios,

Tan D = AB/BD

Tan (90-x) = h/9

Cot x = h/9 \boxed[tan(90-A)=cotA

1/tan x = h/9

h = 9/tan x

tan x = 9/h ——(2)

From (1) and (2)

h/4 = 9/h

h^{2}= 9*4

h^{2}= 36

h = \sqrt{36}

h = 6

The height of Tower is 6m

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Answered by streetburner
36

Answer:

6 m

Step-by-step explanation:

Let the angles be α & β .

Given :

α + β = 90°

So, β = 90° - α

tan β = tan(90° - α) = cot α .....(1)

From figure,

tan α = h/4 &

tan β = h/9 [from (1)]

So,

(tan α )×(tanβ ) = (h/4)*(h/9)

(tan α )×(cot α) = (h/4)*(h/9)

1 = h²/36

h = ± 6

Since, -6 is not possble .

So, Height of tower = 6 m

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