Question

A surveyer wants to find the distance from points A and B and to an inaccessible point C. These three points form a triangle. Because points he can be cited from both A and B, he knows that the measure of angle a equals 65°. Also, it is known that the distance from A-to-C is 90 m and the distance from B to C is 120 m. What is the measure of angle B

Answer 1

Answer:

42.8°

Step-by-step explanation:

The sine rule states that for a triangle with lengths of a, b and c and the corresponding angles which are opposite the sides as A, B and C, then the following rule holds:

$\frac{a}{sin(A)}=\frac{b}{sin(B)} =\frac{c}{sin(C)}$

Given that points A, B and C forms a triangle with angle A = 65°, distance from A-to-C = 90 m and the distance from B to C = 120 m.

The distance from A to C is the side opposite to angle B. Hence let b =  distance from A to C = 90 m.

The distance from B to C is the side opposite to angle A. Hence let a =  distance from B to C = 120 m.

Therefore using sine rule:

$\frac{a}{sin(A)}=\frac{b}{sin(B)} \\\\\frac{120}{sin(65)}=\frac{90}{sin(B)} \\\\sin(B)=\frac{90*sin(65)}{120} \\\\sin(B) =0.6797\\\\B=sin^{-1}(0.6797)\\\\B=42.8^o$