Unit 8 Exam Review

Pre-Calculus Honors Unit 8 Review Answer Key

1.  List the given cases where the Law of Sine’s is the most appropriate method to use to solve for a triangle and when the Law of Cosine’s is the most appropriate method to use to solve for a triangle.

Law of Sines / Law of Cosines
ASA
AAS
SSA (Ambiguous Case) / SSS
SAS

2. Which case do you have to check if 0, 1, or 2 triangles can be formed? SSA

In your own words, explain how you decided if 1 triangle is formed or if 2 triangles may be formed using the given information? When you take the inverse of sine you are given the angle in quadrant 1 and must find the supplementary pair angle. If the sum of the given angle and the supplementary pair angle is greater than 180 degrees you have 1 triangle. If the sum is less than 180 degrees you have 2 triangles. If you get error when taking the sine inverse you have 0 triangles.

In 3-6, find the remaining angle(s) and side(s) of each triangle, if it exists. If no triangle exists, say “No triangle”. Round answers to one decimal place.

Unit 8 Exam Review

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Unit 8 Exam Review

7. A pilot has just started on the glide path for landing at an airport with a runway length of 1.7 miles. The angles of depression from the plane to the ends of the runway are 19.4 degrees and 20.7 degrees

(a)  Draw a diagram that visually represents the problem

(b)  Find the air distance the plane must travel until touching down on the near end of the runway. 24.9 miles

(c)  Find the ground distance the plane must travel until touching down on the near end of the runway. 23.3 miles

(d)  Find the altitude of the plane when the pilot begins descending.

8.8 miles

Challenge #1: In the figure below, a beam of light is directed at the blue mirror, reflected to the red mirror, and then reflected back to the blue mirror. Find the distance PT, which the light travels from the red mirror to the blue mirror.

Step 1 Find PQ = 2.64

Step 2 Find

Step 3 Find < OPQ = 106.2 degrees

Step 4 Find

Step 5 Find <TPQ = 106.2-73.8 = 32.4 degrees

Step 6 Find PT using the Law of Sines = 2.01 feet

Challenge #2: Find the missing lengths and angle measurements in the figure below. Round all answers to the nearest tenth.