Question

1. to find the distance ca across the river a length cb of 50 meters was measured on one bank. the measure of ∠b was found to be 34°10. angle c is a right angle. how long is ca?

Explanation:

Step1: Convert angle to decimal degrees

We know that $10'=\frac{10}{60}\approx0.1667^{\circ}$, so $34^{\circ}10' = 34 + \frac{10}{60}\approx34.1667^{\circ}$.

Step2: Use tangent function

In right - triangle $ABC$ with $\angle C = 90^{\circ}$, $\tan B=\frac{CA}{CB}$. Given $CB = 50$ m and $B\approx34.1667^{\circ}$, we have $CA=CB\times\tan B$.

Step3: Calculate the value of $CA$

$CA = 50\times\tan(34.1667^{\circ})$. Since $\tan(34.1667^{\circ})\approx0.677$, then $CA=50\times0.677 = 33.85$ m.

Answer:

$33.85$ m