# Math Help - [SOLVED] Sine and Cosine Rule

1. ## [SOLVED] Sine and Cosine Rule

To find the breadth of a river, an observer stands at a point B on one bank and notes a point A directly across on the opposite bank.

He then measures a distance BC of 36m in AB produced, and next walks a distance CD of 120m at right angles to AC.

He then finds that AC subtends an angle of 56 degrees 20 minutes. at D. Find the breadth of the river, and the angle which AB subtends at D.

I am having trouble interpreting this question.

2. Have you drawn a picture? You actually have two right triangles, ACD and BCD.

And, because they are right triangles you don't need either the "sine rule" or "cosine rule".

Call the distance across the river "x". Then the total distance AC is 36+ x meters. That is the leg of the right triangle ACD opposite angle D. The "near side" has length 120 m. Solve the equation $\frac{x+ 36}{120}= tan(56^o 20')$.

Call the angle that BC (NOT AB) subtends at D " $\theta$". Then it is an angle of right triangle BCD with "opposite" side of length 36 m and "near side" of length 120 m. $tan(\theta)= \frac{36}{120}$. Once you have solved that for $\theta$, the angle AB subtends at D is 56 degrees 20 minutes minus $\theta$.

3. Thanks. I got the answer