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Can anyone help me with this:

A tower 60m high stands on the top of hill. from a point on the ground at sea level, the angles of elevation of the top and bottom are 49 and 37 degrees. find the height of the hill.

A tower 60m high stands on the top of hill. from a point on the ground at sea level, the angles of elevation of the top and bottom are 49 and 37 degrees. find the height of the hill.

In the future please post any Mathematics questions in the Maths section of Academic Help, not in here - this forum is meant for University discussions, eg. course choices, etc.

Hello!

T = top of tower.

B = bottom of tower

P = point on the ground at sea level

H = point at sea level that's directly under the tower (i.e. inside the hill)

Draw a diagram, and you end up with two triangles; one of them goes PHB where angle PHB = 90*

Another goes PBT and is non-right angled, with BT=60m.

* means "degrees" (sorry)

You want to find HB

angle TPH = 49*

angle BPH = 37*,

so angle BPT = 12* and

BPH is a right angled triangle so HBP=53*

Also PBT = 127* (makes straight line with HBP)

Angle PTB = 41*

Using the sine rule on the top triangle PBT,

(sin 12) /60 = (sin 41) / PB

So

PB = (sin 12) / (60 sin 41)

Using the lower triangle PHB,

HB/PB = sin 37

So HB = PB sin 37

and HB = [(sin 12)/(60 sin 41)] sin 37

(No calc on me, so I can't give you an answer to 3sf, but there you go)

Love

Danniella

T = top of tower.

B = bottom of tower

P = point on the ground at sea level

H = point at sea level that's directly under the tower (i.e. inside the hill)

Draw a diagram, and you end up with two triangles; one of them goes PHB where angle PHB = 90*

Another goes PBT and is non-right angled, with BT=60m.

* means "degrees" (sorry)

You want to find HB

angle TPH = 49*

angle BPH = 37*,

so angle BPT = 12* and

BPH is a right angled triangle so HBP=53*

Also PBT = 127* (makes straight line with HBP)

Angle PTB = 41*

Using the sine rule on the top triangle PBT,

(sin 12) /60 = (sin 41) / PB

So

PB = (sin 12) / (60 sin 41)

Using the lower triangle PHB,

HB/PB = sin 37

So HB = PB sin 37

and HB = [(sin 12)/(60 sin 41)] sin 37

(No calc on me, so I can't give you an answer to 3sf, but there you go)

Love

Danniella

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