Question

In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.

Answer 1

Answer: $x\approx182\ ft$

Step-by-step explanation:

For this exercise you need to use the following Trigonometric Identity:

$cos\alpha =\frac{adjacent}{hypotenuse}$

Observe the Right triangle BCD given in the exercise. You can identify that, in this case:

$\alpha =\angle C=77\°\\\\adjacent=CD=41\ ft\\\\hypotenuse=BC=x$

Knowing these values, you can substitute them into  $cos\alpha =\frac{adjacent}{hypotenuse}$, as below:

 $cos(77\°)=\frac{41}{BC}$

The next step is to solve for "x" in order to find its value:

$x*cos(77\°)=41\\\\x=\frac{41}{cos(77\°)}\\\\x=182.26\ ft$

Finally, rounded the result to the nearest foot, you get that this is:

$x\approx182\ ft$