Answer
(a) 3.77 mi
(b) 2.00 mi
Work Step by Step
(a)
1. If the plane's trajetory is parallel to the ground, then, for the red triangle:
$$\angle B = 48^o$$
Distance of the plane from point A = b
And if $C$ is the point at the plane:
$$32^o + 48^o + \angle C = 180^o $$ $$\angle C = 180^o - 32^o - 48^o = 100^o$$
- Using the law of sines:
$$\frac{sin \space B}{b} = \frac{sin \space C} c$$ $$b = c \space \frac{sin \space B}{sin \space C} = (5 \space mi)\frac{sin \space 48^o}{sin \space 100^o} = 3.77 \space mi$$
(b)
Considering a right triangle with vertices: A, C and another one in the ground right below the plane, which i am going to call "D", the elevation of the plane is represented by $a$.
$$\angle A = 32 ^o$$
Using the law of sines:
$$a = d \space \frac{sin \space A}{sin \space D} = (3.77 \space mi) \frac{sin 32^o}{sin90^o} = 2.00 \space mi$$
