Question

Use the table and the dimensions given in the diagram below. What is the approximate angle of descent?

Answer 1

Look at the figure.
For angle A, the side measuring 3.4 mi is the opposite or the adjacent leg?

Answer 2

The important thing to realize here is that the angle of descent (or depression, actually) is the same as the tiny angle going up from the base to the plane, the interior angle that is not 90. You are given the side opposite that angle and the hypotenuse which makes very good use of our sin identity! The sin of the angle is 3.4/10, which is .34

Answer 3

Its opposite right?

Answer 4

Correct.
Now the next side we have a length is the 10 mi. side. That is the hypotenuse of the triangle.
Which trig function relates the opp and the hyp?

Answer 5

sin

Answer 6

Do you know SOH CAH TOA?

Answer 7

Yeah

Answer 8

Correct.
We now have:

\(\sin A = \dfrac{3.4}{10} = 0.34\)

Answer 9

Now you look up the given table under sin.
Which angle has a sine value close to 0.34?

Answer 10

20

Answer 11

Great.
That means angle A measure approx. 20 deg.

Answer 12

I get it. Thanks!

Answer 13

I called the angle of descent x in the figure above.
Since the two horizontal lines are parallel, angles x and A are congruent since they are alternate interior angles.
That makes x = A = 20.