Problem

$\theta$ is an angle in a right-angled triangle. \[ \tan \theta=\frac{23}{52} \] What is the value of $\theta$ ? Give your answer in degrees to 1 d.p.

Solution

Step 1 :Given that \(\tan \theta = \frac{23}{52}\)

Step 2 :Use the inverse tangent function (arctangent) to find the angle: \(\theta = \arctan(\frac{23}{52})\)

Step 3 :Calculate the angle in radians: \(\theta \approx 0.4164\) radians

Step 4 :Convert the angle to degrees: \(\theta \approx 23.8602\) degrees

Step 5 :Round the angle to 1 decimal place: \(\boxed{23.9}\) degrees

From Solvely APP
Source: https://solvelyapp.com/problems/37761/

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