http://www.ck12.org Chapter 4. Basic Triangle Trigonometry
Greek lettersalphaandbeta(α,β)are often used as placeholders for known angles. Unknown angles are often
referred to asθ(theta).
ASArefers to the situation from geometry when there are two known angles in a triangle and one known side that is
between the known angles.
Guided Practice
- The angle of depression of a boat in the distance from the top of a lighthouse is 10 π. The lighthouse is 200 feet tall.
Find the distance from the base of the lighthouse to the boat. - From the third story of a building (50 feet) David observes a car moving towards the building driving on the
streets below. If the angle of depression of the car changes from 21◦to 45◦while he watches, how far did the car
travel? - If a boat travels 4 miles SW and then 2 miles NNW, how far away is it from its starting point?
Answers: - When you draw a picture, you see that the given angle 10 π is not directly inside the triangle between the lighthouse,
the boat and the base of the lighthouse. It is complementary to the angle you need.
π
10 +θ=π
2
θ=^25 πNow that you have the angle, use tangent to solve forx.
tan^25 π= 200 x
x=200 tan^25 π≈ 615. 5 ...f tAlternatively, you could have noticed that 10 π is alternate interior angles with the angle of elevation of the lighthouse
from the boat’s perspective. This would yield the same distance forx.
- Draw a very careful picture: