Question

A beam of gamma rays is to be used to treat a tumor known to be 1.8cm beneath the patients skin to avoid damaging a vital organ the radiologist moves the source over 5.3 cm at what angle to the patient's skin must the radiologist aim the gamma ray source to hit the tumor?

Answer 1

Answer:

  about 18.8°

Step-by-step explanation:

The depth of the tumor (1.8 cm) is the leg of the right triangle that is opposite the angle of interest. The offset distance (5.3 cm) is the adjacent leg of the triangle.

We know that ...

  tan(angle) = opposite/adjacent = (1.8 cm)/(5.3 cm) = 18/53

Then the angle is found from ...

  angle = arctan(18/53) ≈ 18.76°

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The arctangent, or inverse of the tangent function, is also written tan⁻¹. It may be a "second function" of your calculator's tan key.