Questions: Take the interse cosine of both sides cos B = 65/70

Solution Steps

To find the angle \( B \) given the cosine value, we need to use the inverse cosine function (also known as arccosine). This will allow us to determine the angle whose cosine is \(\frac{65}{70}\).

Given: \[ \cos B = \frac{65}{70} \] Simplify the fraction: \[ \cos B = \frac{13}{14} \approx 0.9286 \]

Use the inverse cosine function to find \( B \) in radians: \[ B = \arccos\left(\frac{13}{14}\right) \approx 0.3803 \text{ radians} \]

Convert the angle from radians to degrees: \[ B \approx 0.3803 \times \frac{180}{\pi} \approx 21.79^\circ \]

Final Answer