# Two observers A and B are 100 ft apart and working at an object X above them. How far is object from observer A if angle B is 30 degrees and angle A is 45 degrees

1
by rjay36

• Brainly User
2016-03-11T23:26:58+08:00

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Angle from object X = 180° - (∠A + ∠B)
= 180° - (45° + 30°)
= 180° - 75°
=105°

∠X = 105°
x (side opposite X) = 100 ft.
∠A = 45°
a (side opposite A)= distance from B to X
∠B = 30°
b (side opposite B) = distance from A to X

Solve using Law of Sines:

1).  Solve for a, or the distance from B to Object X.
x           a
-------- =  -------
sin X      sin A

100 ft               a
--------------  = ---------
sin 105°         sin 45°

a (sin 105°) = 100 ft (sin 45°)

100 ft (sin 45°)
a = ----------------------
sin 105°

100 ft (0.707)
a = --------------------
0.966

70.7 ft
a = -------------
0.966

a =  73.19 ft or 73 ft  ⇒ distance from B to Object X.

2.)  Solve for b, or the distance from A to Object X:

100 ft (sin 30°)
b = -------------------
sin 105°

100 ft (0.5)
b = -----------------
0.966

50 ft
b = -----------
0.966

b =  51.75 or 52 ft. ⇒ distance from A to Object X.

ANSWER:  The distance from observer A to Object X is 52 ft, while the distance from observer B to to Object X is 73 ft.