Download Right Triangle Trigonometry

Right Triangle Trigonometry
1
Pearson Ch 7
Exercise 7.1 p217
Q38, 39, 40 - 45
Homework Tip: Don’t ask
Labeling Convention for Triangles
A
This angle can be identified as:
ÐA, ÐCAB, ÐBAC, Â, q
θ
c
b
C
a
*The sides labeled ‘a’ and ‘b’ are called
“legs”, and the side labeled ‘c’ is called
the “hypotenuse”.
B
Notes:
- Capital letters are used at the vertices of the triangle
- The corresponding lower case letter is used for the side opposite the angle
- Greek letters are used to label angles on the inside of the triangle
Pythagorean
Theorem
Q1: For this triangle, find the length of side a.
c = a +b
2
2
2
12
5
a
Trigonometric Ratios
*Memory Aid – SOH CAH TOA
Looking at the trigonometric ratios, what generalization can be made about the tan ratio?
Q2: For this triangle, find the length of side a.
Q3: Find the size of ∠B in this triangle.
Special Right-Angled Triangles and Exact
Values
There are two special triangles for which you can easily determine (and need to know)
the EXACT VALUES of the trigonometric ratios:
45°-45°-90°
θ
0°
30°
45°
60°
30°-60°-90°
90°
sinθ
cosθ
tanθ
Angles of Elevation &
Depression
Q5: The angle of depression from the roof of building A to the foot of a second
building, B, across the same street and 40 meters away is 65°. The angle of elevation
of the roof of building B to the roof of building A is 35 °. How tall is building B?
Q6: Xin is at Shanghai airport watching the planes take off. He observes a plane that is at an
angle of elevation of 20 ° from where he is standing at point G. The plane is at a height of 350
metres. This information is shown in the following diagram.
a)
Calculate the horizontal distance, GH,
of the plane from Xin.
The plane took off from a point T, which is 250 metres from
where Xin is standing, as shown in the following diagram.
b) Calculate the angle ATH, the takeoff angle of the plane.
Bearings
Bearings are a navigation convention for describing direction. Bearings are always
measured clockwise from North. Bearings are written as 3 numbers (so they were
easy to see in ships logs).
Q4: Find the angle 𝛉 in the diagram shown.
Note that ∠ACB ≠ 90∘
Bearings
Q7: Janette walks for 8 km on a bearing of 045° and then 11 km on a bearing of 135°.
Find the distance and bearing from her starting point.