## Trigonometry 7th Edition

The person is $1377$ ft from the building when she makes her second observation.
Find the angles of the larger triangle that includes both triangles $\angle A = 90˚$ $\angle B = 28˚$ $\angle C = 180 - (90+28)$ $= 62˚$ 2. Find the angles inside the smaller triangle on the left side $\angle A = 180 - 38$ $= 142˚$ $\angle B = 28˚$ $\angle C = 180 - (142 + 28$ $= 10˚$ 3. Find the angles inside the large triangle on the right side $\angle A = 90˚$ $\angle B = 38˚$ $\angle C = 62 - 10 = 52˚$ 4. Use the sine law to solve for the missing length of the small triangle on the left $\frac{x}{sin(28)} = \frac{440}{sin(10)}$ $x = \frac{440sin(28)}{sin(10)}$ by GDC / calculator $x = 1189.574....$ft 5. Use the answer in #4 to solve for the missing angle in the large triangle $\frac{y}{sin(52)} = \frac{1189.574...}{sin(90)}$ $y = \frac{1189..sin(52)}{1}$ $y = 937.39...$ ft 6. Add up the previous length with the known length of $440$ ft $= 937.39... + 440$ $=1377$ ft Therefore the person is $1377$ ft from the building when she makes her second observation.