Question

The radius of the circle below intersects the unit circle at (Three-fifths, four-fifths). What is the approximate value of Theta? A unit circle is shown. A radius with length 1 forms angle theta in quadrant 1. [Not drawn to scale] 0. 6 radians 1. 0 radians 36. 9 degrees 53. 1 degrees.

Answer 1

The measured value of Theta is  53.1 degrees.

Given

The radius of the circle below intersects the unit circle at (3/5, 4/5).

What is tan theta?

The measure of the tan angle is defined as the ratio of perpendicular by the base.

The measure of the tan theta is;

$\rm Tan\theta=\dfrac{x}{y}$

Where the value of x is 3/5 and y is 4/5.

Substitute all the values in the formula

$\rm Tan\theta=\dfrac{x}{y}\\\\\rm Tan\theta=\dfrac{\dfrac{4}{5}}{\dfrac{3}{5}}\\\\\\Tan\theta = \dfrac{4}{5} \times \dfrac{5}{3}\\\\Tan \theta=\dfrac{4}{3}\\\\\theta=tan{-1}(\dfrac{4}{3})\\\\\theta=53. 1 \ degrees$

Hence, the measured value of Theta is  53.1 degrees.

To know more about Trigonometric ratios click the link given below.

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