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HW-pg. 537-538 (1-15, 20)
5.8, 8.2-8.4 assessment next Friday 2-22-13
www.westex.org HS, Teacher Website
2-15-13
Warm up—Geometry CPA
1. Find BC. Round to the nearest tenth.
A
32o
9
B
C
GOAL:
I will be able to:
1. use trigonometric ratios to find angle measures in
right triangles and to solve real-world problems.
HW-pg. 537-538 (1-15, 20)
5.8, 8.2-8.4 assessment next Friday 2-22-13
www.westex.org
HS, Teacher Website
Name _________________________
Geometry CPA
8-3 Solving Right Triangles
Date ________
San Francisco, California, is famous for its steep streets. The steepness
of a road is often expressed as a percent grade. Filbert Street, the
steepest street in San Francisco, has a 31.5% grade. This means the road
rises 31.5 ft over a horizontal distance of 100 ft, which is equivalent to a
17.5° angle. You can use trigonometric ratios to change a percent grade to
an angle measure.
Example 1: Identifying Angles from Trigonometric Ratios
Use the trigonometric ratio
to determine which angle of the triangle is A.
YOU TRY:
Use the given trigonometric ratio to determine which angle of the triangle is A.
a.
b. tan A = 1.875
In Lesson 8-2, you learned that sin 30° = _____. Conversely, if you know that the sine of an
acute angle is 0.5, you can conclude that the angle measures _____. This is written as
_______________.
If you know the sine, cosine, or tangent of an acute angle measure, you can use the inverse
trigonometric functions to find the measure of the angle.
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)
YOU TRY:
Use your calculator to find each angle measure to the nearest degree.
a. tan-1(0.75)
b. cos-1(0.05)
c. sin-1(0.67)
Using given measures to find the unknown angle measures or side lengths of a triangle is known
as _______________ ___ __________. To solve a right triangle, you need to know two
side lengths or one side length and an acute angle measure.
Example 3: Solving Right Triangles
Find m<R. Round to the nearest degree.
YOU TRY:
Find m<F. Round to the nearest degree.
Example 4: Solving a Right Triangle in the Coordinate Plane
The coordinates of the vertices of ∆PQR are P(–3, 3), Q(2, 3), and R(–3, –4). Find the
side lengths to the nearest hundredth and the angle measures to the nearest degree.
y
x
YOU TRY:
The coordinates of the vertices of ∆RST are R(–3, 5), S(4, 5), and T(4, –2). Find the
side lengths to the nearest hundredth and the angle measures to the nearest degree.
y
x
Example 5: Travel Application
A highway sign warns that a section of road ahead has a 7% grade. To the nearest
degree, what angle does the road make with a horizontal line?
A 7% grade means the road rises (or falls) 7 ft for every 100 ft of horizontal distance.
YOU TRY:
Baldwin St. in Dunedin, New Zealand, is the steepest street in the world. It has a grade
of 38%. To the nearest degree, what angle does Baldwin St. make with a horizontal line?
8-3 Practice
Use your calculator to find each angle measure to the nearest degree.
1. cos-1 (0.97)
2. tan-1 (2)
3. sin-1 (0.59)
Find the unknown measures. Round lengths to the nearest hundredth and angle measures
to the nearest degree.
4.
5. The coordinates of the vertices of ∆MNP are M (–3, –2), N(–3, 5), and P(6, 5). Find
the side lengths to the nearest hundredth and the angle measures to the nearest degree.
y
x