Right triangles Trigonometry 7.5-7.6 DAY 1

1
Right triangles Trigonometry7.5-7.6DAY 1
2
A trigonometric ratio is a ratio of the lengths
of two sides of a right triangle. We will use
three different ratios, sine, cosine and
tangent.
3
Remember Chief Sohcahtoa
Trigonometric Ratio Abbreviation Definition
Sine of A Sin A opp. ?A a Hypotenuse c
Cosine of A Cos A adj. to ?A b Hypotenuse c
Tangent of A Tan A opp. ?A a adj. to ?A b
4
Examples Using Sohcahtoa
1.
sin A sin B cos A cos B tan A
tan B
5
Examples

• Use a calculator. Find the following, rounding
  to 4 decimal places.
• sin 27? B) tan 32?
• C) cos 72? D) sin 48?

.4540
.6249
.7431
.3090
mode!
6
Examples

• Find the measure of the acute angles given the
  same trigonometric ratio.
• A) sin B B) cos E C) tan I

62
X 67.38 67
36.89 37
inverse function
How can I find angles with this????
2nd
sin
15/17
7
Tan 50 x / 4.8
8
angles of elevation and DepressionDAY 2
9
7-7 Angles of Elevation and Depression

• By definition, the picture at the left shows each
  of the angle of depression and the angle of
  elevation. However, since the angles are
  congruent because ________________________________
  ___, we can just use the triangle at the right

the lines are ll, then Alternate Interior angles
are congruent
10
Class Exercises

• A surveyor is 130 ft. from a tower. The tower is
  86 ft. high. The surveyors instrument is 4.75
  feet above the ground. Find the angle of
  elevation.
• 2. A plane P is 3 miles above ground. The pilot
  sights the airport A at an angle of depression of
  15o. He sights his house H at an angle of
  depression of 32o. What is the ground distance d
  between the pilots house and the airport.

Tan x (86-4.75)/130 Tan x 81.25/130 Tan x
.625 X 32
86 ft
Angle of elevation ??
130 ft
4.75 ft
Airport distance Tan 15 3/a a 3/tan 15 a
11.2 miles
Home distance Tan 32 3/h h 3/tan 32 h 4.8
miles
15
3 miles
32
32
15
Airport home 11.2 - 4.8 6.4 miles
11
Class Exercises

• State an equation that would enable you to solve
  each problem. Then solve. Round answers to the
  nearest tenth.
• Given m?P 15 and PQ 37, find QR.
• b. Given PR 2.3 and PQ 5.5, find m?P.

Sin 15 x/37 37 sin 15 x
9.6 x
Cos P 2.3/5.5 Cos P .41818
P 65.3
12
Class Exercises

• A truck is driven onto a ramp that is 80 ft long.
  How high is the end of the ramp when the angle
  of elevation of the ramp is ?
  
• ?

Sin 30 x/80 80 sin 30 x
Sin 45 x/80 80 sin 45 x
80 ft
X ft
56.6 Ft x
40 Ft x
30
13
Class Exercises

• 5. A 6 ft tall person is enjoying a Saturday
  afternoon by flying a kite. The angle of
  elevation from him to the kite is . He
  brought 75 ft of string and has used all of it.
  How high is the kite?

75 ft
x ft
35
Sin 35 x/75 75 sin 35 x
6 ft
43 ft x
The kite is 43 6 49 ft above the ground.
14
System of equations with trig

• You are in a building on the 3rd floor and look
  across the street at a crane. You notice that
  the angle when you look up at the top of the
  crane is 55 and the angle when you look down to
  the bottom is 61. If the crane is 60 ft tall,
  how far away is the building you are in ?

Step 1 Write the 2 equations for the
system. Step 2 Solve each equation for y. Step
3 Set the equations equal to each other and
solve for x. Step 4 If you need the answer
for y plug in the value for x and solve for y.
ft away from the crane