Wow! What a beautiful tree. I wonder how tall it is?
Of course! I would love to help!
Hey mum! Can you help me conduct some measurements to see how tall the tree is?
I know your eye height is 1.67 metres, so all we have to find are the other lengths.
In order to find the height of the tree, we need to measure the height of my eyes to the floor, the distance from the tree to myself and the angle of elevation.
Perfect! Now I know those lengths I can work out the height of the tree. Thanks mum.
I have finished measuring all the lengths we need and I can tell you that the distance from the tree to you is 7.2 metres and the angle of elevation is 67 degrees.
So, tan(67) = x/7.2. If I multiply both sides by 7.2, that means 7.2tan(14) = x! So that means x = 17.0 to 1 decimal place. Adding my height on means 17.0 + 1.67 = 18.67 which rounded off to the nearest decimal place is 18.7 metres.
Hmm... If I have the adjacent length (7.2) and have to work out the opposite length (x), that means I have to use the tangent ratio.
Hey mum! The tree is approximately 18.7 metres tall!
Awesome work Daniel! And perfect timing too. Its time for dinner. Come on, lets go inside.