Final answer:
The value of θ in a right triangle where tan θ = 23/52 is found using the inverse tangent function, usually with a calculator set to degree mode.
Step-by-step explanation:
The student is asking to find the value of an angle in a right-angled triangle when given the tangent of the angle. The tangent (tan) of an angle in a right triangle is the ratio of the opposite side to the adjacent side. In this case, the tan θ = 23/52. To find the angle θ, you would use the inverse tangent function, also known as arctan or tan-1.
To find the value of θ, you would calculate:
θ = tan-1(23/52)
You would typically use a calculator to perform this computation which would give the answer in degrees. Make sure the calculator is set to the correct mode (degrees rather than radians) when you perform the calculation. The result will give you the angle θ to one decimal point accuracy.