The value of the tangent of the measure of the angle QSR is equal to √3 / 3.
What is the exact value of a tangent function?
Tangent function is a kind of trigonometric functions, a kind of trascendent function, that is, a function that cannot be described in algebraic terms. The angles QST and QSR represent a linear pair, then:
m ∠ QST + m ∠ QSR = 180°
150° + m ∠ QSR = 180°
m ∠ QSR = 30°
Hence, the measures of the remaining angles of the triangle QSR are, respectively:
m ∠ SQR = 60°, m ∠ SRQ = 90°
By geometry we know that the length of the long leg (SR) is √3 / 2 times the length of the hypotenuse and the length of the short leg (QR) is 1 / 2 times the length of the hypotenuse.
Then, by definition of tangent and 30 - 60 - 90 triangle properties:
tan m ∠ QSR = QR / SR
tan m ∠ QSR = (r / 2) / (√3 r /2), where r is the length of the hypotenuse.
tan m ∠ QSR = √3 / 3
The value of the tangent of the measure of the angle QSR is equal to √3 / 3.
To learn more on trigonometric functions: https://brainly.com/question/6904750
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