Geometry question:
Tommy cycles from his home to his school as shown in the diagram. The Journey has a total distance of 9km. Two kilometres into his journey, he passes his local shop.
Find to the nearest metre:
(i) The distance between the shop and the park.
(ii) The distance between the school and the park

Question

Geometry question:
Tommy cycles from his home to his school as shown in the diagram. The Journey has a total distance of 9km. Two kilometres into his journey, he passes his local shop. 
Find to the nearest metre:
(i) The distance between the shop and the park.
(ii) The distance between the school and the park

photon336 · Answer

Hey, did they give you a diagram?

anonymous · Answer

|dw:1460494429453:dw|

anonymous · Answer

I have already figured out they are similar triangles

anonymous · Answer

Similar triangles proof:
Let the angle from shop to park to home = x i.e
|dw:1460494935385:dw|
Since, the total degrees in a triangle is 180 degrees this means the reamining angle must be 90-x |dw:1460495062393:dw|
But, the angle between school, Park and home is also 90 degrees|
dw:1460495176566:dw|
That must mean that the angle between school Park and shop is 90-x
|dw:1460495296574:dw|
Therefore, we have 2 angles equal(90-x) , 2 sides equal (from shop to Park same length). 
Now if we have (90-x ) + 90  + x in one triangle,  and 90 + 90-x in the other triangle, the third angle in the other triangle must be x, so we have similar triangles