Help-me-Observe-points-A-B-and-C-below-and-find-the-widthof-a-lake-according-to-the-following-data-AB-m-C-39-52-12-BC-257-5-m-A-97-7-56-CA-30-m-B-42-59-52-CA-is-t

Question Number 203321 by SonGoku last updated on 16/Jan/24

Help - me!

Observe points A, B and C below and find the widthof a lake according to the following data :

(AB) m; \hat{C} = 39 ° 52^{'} 12^{″}

(BC - 257.5) m; \hat{A} = 97 ° 7^{'} 56^{″}

(CA - 30) m; \hat{B} = 42 ° 59^{'} 52^{″}

CA is the width of the lake

∙^{C}

∙_{A}

∙_{B}

Answered by esmaeil last updated on 17/Jan/24

1^{o} = 60^{^{'}} = 3600^{∥} \to

\overset{\land}{C} = 39 + (\frac{52}{60} + \frac{12}{3600}) = 39 . 87^{o}

\overset{\land}{B} = 42 + (\frac{59}{60} + \frac{52}{3600}) \approx 42.9978

\frac{A B}{s i n c} = \frac{A C}{s i n B} \to A B = \frac{s i n (39.87)}{s i n (42.9987)} \times 30

= 28.1993

Facebook Tweet Pin