Question

assume that θ is an acute angle in a right - triangle satisfying the given condition. evaluate the remaining trigonometric functions.
sin θ = 3/8
cos θ = √55/8
(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 formula

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

Step2: Substitute given values

Given $\sin\theta = \frac{3}{8}$ and $\cos\theta=\frac{\sqrt{55}}{8}$, then $\tan\theta=\frac{\frac{3}{8}}{\frac{\sqrt{55}}{8}}$

Step3: Simplify the expression

$\tan\theta=\frac{3}{8}\times\frac{8}{\sqrt{55}}=\frac{3}{\sqrt{55}}=\frac{3\sqrt{55}}{55}$

Answer:

$\frac{3\sqrt{55}}{55}$