Linda and Ali are standing on a riverbank, at points A and B respectively. Ali is 170 meters from a house located across the river at point C. Suppose that angle A (angle BAC) is 44°, and angle B (angle ABC) is 53°. How far are Linda and Ali standing from one another? Round your answer to the nearest tenth of a meter.

Using the Law of Sines, we calculated the distance between Linda and Ali (A and B) based on the angles and distance to a house. After performing the calculations, the distance found is approximately 211.1 meters. This is rounded to the nearest tenth of a meter.
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Answered by Anonymous | 2025-07-10

To find the distance between Linda and Ali, we can use the Law of Sines, which is applicable in any triangle and is especially useful in solving problems involving non-right triangles like this one.
Given:

Angle A ( ∠ B A C ) = 44°
Angle B ( ∠ A BC ) = 53°
Distance AC = 170 m

We are interested in finding the distance AB, which we will call c .

First, we determine angle C ( ∠ A CB ) using the angle sum property of triangles:
∠ C = 180° − ∠ A − ∠ B ∠ C = 180° − 44° − 53° = 83°

Now, apply the Law of Sines, which states:
sin A a ​ = sin B b ​ = sin C c ​
For c (which is AB), we use:
sin 83° c ​ = sin 53° 170 ​

Solve for c :
c = sin 53° 170 × sin 83° ​

Calculate the numerical values:

sin 83° ≈ 0.9934
sin 53° ≈ 0.7986


Substitute these values into the equation:
c = 0.7986 170 × 0.9934 ​

Perform the computation:
c ≈ 0.7986 169.878 ​ c ≈ 212.7


Therefore, the distance between Linda and Ali is approximately 212.7 meters.
Rounded to the nearest tenth, the distance is 212.7 meters.

Answered by OliviaMariThompson | 2025-07-22