8-3 Solving Right Triangles 8-3 Solving Right Triangles

8-3 Solving Right Triangles
8-3 Solving Right Triangles
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
Geometry

8-3 Solving Right Triangles
Objective
Use trigonometric ratios to find angle
measures in right triangles and to solve
real-world problems.
Holt McDougal Geometry

8-3 Solving Right Triangles
Check It Out! Example 1a
Use the given trigonometric
ratio to determine which
angle of the triangle is A.
Holt McDougal Geometry

8-3 Solving Right Triangles
Finding Angles
1. From the angle you wish to find, which of
the three sides are you given: opposite,
adjacent, or hypotenuse?
22 cm
15 cm
x
Holt McDougal Geometry

8-3 Solving Right Triangles
Finding Angles
2. Given those two sides, use SOH-CAH-TOA
to decide which trig ratio to use: sin, cos,
or tan.
22 cm
15 cm
x
Holt McDougal Geometry

8-3 Solving Right Triangles
Finding Angles
3. Set up an equation using the correct trig
ratio and the correct order of sides.
– NOTE: x is now on the other side with
sin, cos, or tan.
22 cm
15 cm
x
Holt McDougal Geometry

8-3 Solving Right Triangles
Finding Angles
4. This is the most crucial step. You cannot
cross-multiply, because that will not
separate cos from x. Instead you must use
what is called the inverse trig function.
– The symbol for this is sin -1 , cos -1 , or
tan -1 .
Holt McDougal Geometry

8-3 Solving Right Triangles
Finding Angles
• So, use the cos -1 on both sides of the
equation. On the right hand side, cos -1 and
cos cancel, leaving you just x.
• On the left hand side, we must use our
calculators.
Holt McDougal Geometry

8-3 Solving Right Triangles
Finding Angles-Calculator
• Most of you will type it exactly as it is read:
2nd -> cos -> 15 / 22 ) -> Enter
• Others will have to work backwards:
15 / 22 -> Enter -> 2nd -> cos
Holt McDougal Geometry

8-3 Solving Right Triangles
1.
25 cm
5 cm
90
x
Find the value of x
Holt McDougal Geometry

8-3 Solving Right Triangles
2.
Find the value of x
90
17 cm
x
25 cm
Holt McDougal Geometry

8-3 Solving Right Triangles
Find the value of x and y
3.
y
35 in
x
90
22 in
Holt McDougal Geometry

8-3 Solving Right Triangles
4.
Find the value of x, y and z
x
5.8 cm
y
z 90
3.2 cm
Holt McDougal Geometry

8-3 Solving Right Triangles
Example 2: Calculating Angle Measures from
Trigonometric Ratios
Use your calculator to find each angle measure
to the nearest degree.
A. cos -1 (0.87) B. sin -1 (0.85) C. tan -1 (0.71)
cos -1 (0.87) 30° sin -1 (0.85) 58° tan -1 (0.71) 35°
Holt McDougal Geometry