Question

Homework 8.1 Applications Score: 0/5 0/5 answered Question 1 Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point Con land such than ZCAB = 43.8. Find the distance across the lake from A to B. B 5388 43.8° с 338 ft NOTE: The triangle is NOT drawn to scale. ft distance = Enter your answer as a number; your answer should be accurate to 2 decimal places.

Answer 1

Hey there stay home and stay safe.

According to HomeworkLib guidelines I have to solve only the first question when multiple questions are given.So I am solving the first question.

$\triangle ABC $ is a triangle given where\\$ \angle CAB=43.8\degree\\ BC=538 ft\\ AC=338 ft\\ $We'll use sine rule to find the value of AB$\\ \frac{AB}{sin\angle C}=\frac{AC}{sin\angle B}=\frac{BC}{sin\angle A}\\ \Rightarrow \frac{AB}{sin\angle C}=\frac{338}{sin\angle B}=\frac{538}{sin(43.8\degree)}\\ sin\angle B=\frac{338sin(43.8\degree)}{538}=0.419255184\\ \Rightarrow \angle B=24.78757307\\ $We know the sum of all angles of a triangle is 180$\degree\\ So,\angle C=180\degree-(43.8+24.78757307)\degree=111.41242693\degree\\ Now,AB=\frac{BCsin\angle C}{sin\angle A}=\frac{538sin(111.41242693\degree)}{sin(43.8\degree)}=723.6442683\approx723.64\ ft$

And please leave a like. Thank you.