3D Trig CSSA prelim problem (1 Viewer)

[Aysce]

A vertical tower of height h metres stands on horizontal ground. From a point P on the ground due
east of the tower the angle of elevation of the top of the tower is 45°. From a point Q on the ground
due south of the tower the angle of elevation of the top of the tower is 30°. If the distance PQ is 40
metres, find the exact height of the tower.†

Please show working i tried it but didn't work out :/

 

[funnytomato]

h=20?

 

[funnytomato]

call the bottom of the tower point N
note: triangle PNQ is right angled

 

[SpiralFlex]

I drew a nice pretty diagram for you.





First, we need to find . Since it's an isosceles triangle (both base angles of , hence both sides are equal), we know that is

Second we need to find an expression for





Use the power of pythagoras!





metres.

 

[funnytomato]

"You must spread some Reputation around before giving it to SpiralFlex again"


Edit: " a point P on the ground due east of the tower "

 

[SpiralFlex]

"You must spread some Reputation around before giving it to SpiralFlex again"


Edit: " a point P on the ground due east of the tower "

Delicious tomato, I do not deserve the reputation.

 

[funnytomato]

Delicious tomato, I do not deserve the reputation.

lol
i was gonna draw it, then i kinda failed and gave up

 

[SpiralFlex]

lol
i was gonna draw it, then i kinda failed and gave up

Mm, I still think you are a delicious tomato. I fixed the diagram.

 

[MrBrightside]

Spiral is boss at maths.

 

[Aysce]

Ahh i didn't see it from that perspective, thanks!

 

[SpiralFlex]

Ahh i didn't see it from that perspective, thanks!

Nice pun!