The meaning of “射” and “矮”? The body (身) is only one inch (寸), which should mean "矮".

Throwing (委) the arrow (矢), which should mean "射".

What is wrong here?
The body (身) is only one inch (寸), which should mean "矮".


Here are some characters containing「寸」as a semantic component, directly as part of the immediate decomposition or secondarily as part of one of the decomposed components:


得導持尋付尊奪肘專耐


It should be clear that「寸」probably never means inch as part of other characters.「寸」is a depiction of a hand with a mark around the wrist area, and when it contributes meaning to a character, you should treat it as the same meaning as「手・扌」.

秦簡睡・秦51　今楷　


  
  The mark around the wrist area is called「寸口」in the terminology of Traditional Chinese Medicine, and indicates the location where the pulse is taken.「寸」was later used as a unit of length, but it should be clear that this is not its original meaning.
  
  
  Like most other character components, the stand-alone character「寸」developed a wildly different meaning from its role as a component in other characters.
  
  Other components with the same meaning function as「手・扌」include「又」(picture of a right hand),「」(picture of a left hand), and「爪・爫」(picture of a hand pointing downwards).
  


The「身」part of「射」is a graphical corruption, from a merger between「弓」(bow) and「矢」(arrow):

商甲乙1290合集974西周金靜簋集成4273東周・秦石鼓　秦朝簡睡・雜34　今楷　

In the sequence above, Shape #1 is plainly a picture of a bow and arrow. Shape #2 adds a hand「又」, emphasising the action meaning in「射」. Shapes #3-4 show the corruption process of the bow and arrow into「身」. Shape #4 changes「又」into「寸」.


  A character with a similar structure to「射」is「發」(Zhengzhang OC: /*pad/, to shoot arrows > to emit > expand, develop).「發」is comprised of phonetic「癶」(OC: /*paːd/), semantic「弓」, and semantic「殳」(hand holding a striking weapon, emphasising an attacking action).





  Throwing (委) the arrow (矢), which should mean "射".


「矮」(Zhengzhang OC: /*qraːlʔ/, short stature) is comprised of semantic「矢」and phonetic「委」(/*qrolʔ/).


「矢」(arrow [shaft]) is being used as a length measurement here; you can view it as either the length of the arrow itself or a standardised distance for measuring archery prowess. In English, yard, feet, etc. were similar measures of length, taken from actual objects.


Compare some characters describing length or measurement: 短矩矬矱.
There are other characters that use「矢」for the meaning arrow rather than length, measurement.

The sound development is /*qraːlʔ/ > MC: /ʔˠɛX/, 烏蟹切 > Pinyin: ǎi.




References:


季旭昇《說文新證》
小學堂
國學大師


郭沫若《甲骨文合集》
中國社會科學院考古研究所《殷周金文集成》