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there are several shorcuts to calculate sides for right triangles as fresinha said and one on them is 3-4-5

others are 5-12-13 6-8-10 8-15-17 7-24-25 etc

basically all that satisfy pythagorean theorem

here we need to recognize (visually) that hypothenuse 16+9=25 stands approximatelly in 3-4-5 ratio and therefore the explanation follows hypo = 25 therefore height is (15*15)-(9*9)=sqrt144=12

plug in the triangle formula and calculate 300/2=150
_________________

The one who flies is worthy. The one who is worthy flies. The one who doesn't fly isn't worthy

there are several shorcuts to calculate sides for right triangles as fresinha said and one on them is 3-4-5

others are 5-12-13 6-8-10 8-15-17 7-24-25 etc

basically all that satisfy pythagorean theorem

here we need to recognize (visually) that hypothenuse 16+9=25 stands approximatelly in 3-4-5 ratio and therefore the explanation follows hypo = 25 therefore height is (15*15)-(9*9)=sqrt144=12

plug in the triangle formula and calculate 300/2=150

How do you use those shortcuts such as "3-4-5"? Can you be more elabroative?

No dispute on these basics. But how do you show that the corresponding angles are same?

Ok, here we go.

Between triangles PQR and PQS angle PQR = angle PSQ = 90 degree. angle QPS is common. Hence, the third angle QRP equals angle PQS and this also makes triangles PQS and QSR similar.