Answered

[tex]\(\theta\)[/tex] is an angle in a right-angled triangle.

[tex]\[53 \tan \theta = 12\][/tex]

What is the value of [tex]\(\theta\)[/tex]? Give your answer in degrees to 1 d.p.



Answer :

GinnyAnswer
Certainly! Let's solve the given problem step by step.

We start with the equation:

[tex]\[ 53 \tan \theta = 12 \][/tex]

1. Isolate [tex]\(\tan \theta\)[/tex]:

[tex]\[ \tan \theta = \frac{12}{53} \][/tex]

2. Calculate the value of [tex]\(\frac{12}{53}\)[/tex]:

[tex]\[ \tan \theta \approx 0.2264 \][/tex]

3. Find the angle [tex]\(\theta\)[/tex] in radians:

To find the angle [tex]\(\theta\)[/tex], we use the [tex]\(\tan^{-1}\)[/tex] (arctan) function.

[tex]\[ \theta = \tan^{-1}(0.2264) \approx 0.2227 \text{ radians} \][/tex]

4. Convert the angle from radians to degrees:

We use the conversion factor [tex]\(180^\circ / \pi\)[/tex] to convert from radians to degrees.

[tex]\[ \theta \approx 0.2227 \times \frac{180}{\pi} \approx 12.76^\circ \][/tex]

5. Round the answer to 1 decimal place:

[tex]\[ \theta \approx 12.8^\circ \][/tex]

Therefore, the value of [tex]\(\theta\)[/tex] rounded to one decimal place is [tex]\(12.8^\circ\)[/tex].

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