Question

review right triangle tr
2
multiple choicr 1 point
find the exact values of the indicated trigonometric functions. write
fractions in lowest terms.
find sin b and tan b.
sin b = 25/7; tan b = 24/7
sin b = 7/24; tan b = 7/25
sin b = 24/25; tan b = 24/7
sin b = 7/25; tan b = 7/24

Explanation:

Step1: Recall the definitions of sine and tangent in a right - triangle

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\). For angle \(B\), the side opposite to \(B\) is \(AC = 14\), the side adjacent to \(B\) is \(BC=48\), and the hypotenuse \(AB = 50\).

Step2: Calculate \(\sin B\)

\(\sin B=\frac{AC}{AB}\). Substitute \(AC = 14\) and \(AB = 50\). Then \(\sin B=\frac{14}{50}=\frac{7}{25}\) (divide numerator and denominator by \(2\)).

Step3: Calculate \(\tan B\)

\(\tan B=\frac{AC}{BC}\). Substitute \(AC = 14\) and \(BC = 48\). Then \(\tan B=\frac{14}{48}=\frac{7}{24}\) (divide numerator and denominator by \(2\)).

Answer:

\(\sin B=\frac{7}{25};\tan B=\frac{7}{24}\) (the fourth option)