a We can model the path of an airplane by using two sides of a triangle.
Consider that since the distance covered during ascent is the same as the distance covered during descent, this is an isosceles triangle. This is also indicated by the hatch marks on the sides of the triangle. As 90^(∘) <173^(∘) <180^(∘), the angle given on the diagram is obtuse. Since the triangle has an obtuse angle, it is therefore an obtuse triangle.
b We are given that that the angle of ascent and the angle of descent are congruent. Let's indicate this with a marker on the diagram.
Congruent angles have the same measure.
m∠ 1=m∠ 2
We can use the given angle measure and the Triangle Angle-Sum Theorem to set up and solve an equation for m∠ 1.
Since angles ∠ 1 and ∠ 2 are congruent, ∠ 2 has the same measure.
m∠ 1=m∠ 2=3.5 ^(∘)
The measures of the angle of ascent and angle of descent are both 3.5^(∘).
