1. TF.01.4 – Trig. Applications in 3D
MCR3U - Santowski

2. (A) Review Right Angle Trig ratios are:
sin(x) = o/h; cos(x) = a/h; tan(x) = o/a
Sine Law states a/sinA = b/sinB = c/sinC
Cosine Law states a² = b² + c² - 2bcCosA

3. (B) Examples
We will now apply all three methods to problems in 3 dimensions
ex 1. To determine the height of an inaccessible cliff, surveyors recorded the following data: From point A, the angle of elevation to the top of the cliff was 38°. From a second point B 68.5 meters from A, the line of sight between point A and the base of the cliff was 42°. Find the height of the cliff.

4. (B) Examples
ex 2. From the top of a 50 m bridge, two boats are seen at the docks. One boat is seen at S50°W and has an angle of depression of 38° while the second boat is seen at S60°E with a 35° of depression. How far apart are the boats?

5. (B) Examples
ex 3. Two roads intersect at an angle of 12°. Two cars leave the intersection, each on a different road. One car travels 90 km/h and the other 120 km/h. After 20 minutes, a police helicopter 1000m directly above and between the cars sees the slower car at an angle of depression of 14°. What is the horizontal distance from the helicopter to the faster car?

6. (C) Homework Handout from PP-12 text, p236, Q5-10
Nelson text, p522, Q7,14-18