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March 3, 2015

March 3, 2015

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

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 8:18amIn 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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