Question

assume that θ is an acute angle in a right triangle satisfying the given condition. evaluate the remaining trigonometric functions. cos θ = 5/13 sin θ = 12/13 (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) tan θ = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall tangent - sine/cosine relation

$\tan\theta=\frac{\sin\theta}{\cos\theta}$

Step2: Substitute given values

Given $\sin\theta = \frac{12}{13}$ and $\cos\theta=\frac{5}{13}$, then $\tan\theta=\frac{\frac{12}{13}}{\frac{5}{13}}$.

Step3: Simplify the fraction

$\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{13}\times\frac{13}{5}=\frac{12}{5}$

Answer:

$\frac{12}{5}$