Posted by **carlo** on Monday, March 19, 2012 at 7:25am.

howard and keight who are 2km apart are on a horizontal plane observe a balloon in the same vertical plane with themselves the angles of elevation are 50 degrees and 65 degrees respectively find the height of the balloon.

A.if its situated between howard and keight

B.If it is on the side of both of them.

Help plz

- trigonometry -
**Reiny**, Monday, March 19, 2012 at 8:18am
In your sketch, draw an altitude hitting the base line at P, Howard to P is HP, Keight to P is KP

Let HP = x ,angle at H is 50°

then KP = 2-x, angle at K is 65

let the height be h

I see two right - angled triangles,

in the first: cot50 = x/h

x = hcot50

in the second: cot 65 = (2-x)/h

hcot65 = 2-x

x = 2 - hcot65

so

hcot50 = 2-hcot65

hcot50 + hcot65 = 2

h(cot50+cot65) = 2

h = 2/(cot50+cot65)

(only now do we have to go to a calculator, I will let you do the button-pushing)

for the second part, I see it as

cot50 = (2+x)/h and cot 65 = x/h

proceed the same way as above.

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