Question

solve for ( x ). round to the nearest tenth, if necessary.

right triangle abc with right angle at b, ab = 12, angle at c is ( 61^circ ), bc = ( x )

answer
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Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta = 61^\circ$, opposite side $= 12$, adjacent side $= x$.

Step2: Rearrange to solve for $x$

$x = \frac{12}{\tan(61^\circ)}$

Step3: Calculate value

First, find $\tan(61^\circ) \approx 1.8040$
$x \approx \frac{12}{1.8040} \approx 6.65$

Step4: Round to nearest tenth

$x \approx 6.7$

Answer:

$x = 6.7$