What is the approximate value of tan C in a right triangle with sides AB=5, AC=13,...
Check the final answer first, then review the worked steps.
Problem
What is the approximate value of tan C in a right triangle with sides AB=5, AC=13, and BC=13.93?
Answer
0.38
Step-by-step solution
- Identify the sides of the right triangle: The problem provides a right triangle ABC, where angle A is the right angle. The side opposite to angle B is AC, with a length of 13. The side opposite to angle C is AB, with a length of 5. The hypotenuse is BC, with a length of 13.93.
2. Recall the definition of the tangent function: In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. For angle C, the opposite side is AB and the adjacent side is AC.
$$ \tan(C) = \frac{\text{opposite}}{\text{adjacent}} $$
3. Substitute the given values into the tangent formula: Using the lengths of the sides AB and AC, we can calculate the tangent of angle C.
$$ \tan(C) = \frac{AB}{AC} = \frac{5}{13} $$
4. Calculate the approximate value of tan C: Divide 5 by 13.
$$ \frac{5}{13} \approx 0.3846 $$
- Round to the nearest hundredth: The question asks for the approximate value. Rounding 0.3846 to two decimal places gives 0.38.