Question

A plane is descending onto the runway with an angle of depression of 55°. If it has 2.8 miles to go before landing (hypotenuse), what is the current altitude of the plane?
A. 4.9 miles
B. 3.4 miles
C. 4 miles
D. 1.6 miles
E. 2.3 miles

Answer 1

Answer:

Option C is correct

Step-by-step explanation:

Given: A plane is descending onto the runway with an angle of depression of 55°. Also, it has 2.8 miles to go before landing.

To find: current altitude of the plane

Solution:

Consider the attached image.

In ΔABC,

$\angle ACB=55^{\circ}$ (Alternate interior angles)

For any angle $\theta$,

$tan \theta$ = side opposite to angle/side adjacent to angle

$\tan C=\frac{AB}{BC}$

Put $\angle C=55^{\circ}\,,\,BC=2.8\,\,miles$

$AB=2.8\,\tan 55^{\circ}=3.999\approx 4\,\,miles$

So, the current altitude of the plane is 4 miles.

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