Electronic – Measuring distance at angle

Sure, see paragraph 4 about Vishay's fixed-gain receivers:

Many other applications require a reflective sensor that detects not only presence but also proximity by measuring the strength or weakness of the reflected signal. Instead of a fixed detection threshold, analog information from the sensor is needed. This is possible with the TSOP4038, TSOP58038, and TSOP58P38 IR proximity sensors. The length of the sensor’s output pulse in response to the emitter signal varies in proportion to the amount of light reflected from the object being detected. For near objects, the output pulse approaches 100 % of the emitted pulse, for far objects the output pulse becomes shorter.

You will not get the accuracy you need with wifi or Bt. Rssi is not reliable measure. Ultrasonic is an easy answer. Depending on your smartphones microphone frequency response you may get away with just adding an ultrasonic transmitter and use wifi and ultrasonic in tandem to figure out distance. Wifi would be instant and sound will be slower. You may have to pull tricks to eliminate wifi packet delays etc but I see that they can be worked out.