Question

You can sometimes see an eagle gliding with its wings flexed in a characteristic double-vee shape. Each
wing can be modeled as two right triangles as shown in the figure. Find the measure of the angle in the
middle of the wing, to the nearest degree.
H
42 cm
49 cm
33 cm
-
F
G
39 cm
2
E
mZDHG

Answer 1

Using relations in a right triangle, it is found that the measure of angle DHG is of 116º.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

• The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

• The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

• The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, angle DHG is the sum of measures a and b.

Angle a is adjacent to a side of 33 cm, while the hypotenuse is of 49 cm, hence:

$\cos{a} = \frac{33}{49}$

$a = \arccos{\left(\frac{33}{49}\right)}$

$a = 47.66^\circ$

Angle b is opposite to a side of 39 cm, while the hypotenuse is of 42 cm, hence:

$\cos{b} = \frac{39}{42}$

$b = \arccos{\left(\frac{39}{42}\right)}$

$b = 68.21^\circ$

Then:

a + b = 47.66º + 68.21º = 115.87º

Rounding, the measure of angle DHG is of 116º.

More can be learned about relations in a right triangle at https://brainly.com/question/26396675