Transcript Chapter 8.4 and 8.5

CHAPTER 8.4 AND 8.5
Trigonometry and angles of
Elevation and Depression
Inverse Trigonometric Ratios
• Recall that we used sine, cosine, and tangent to find missing
side lengths in right triangles
• We use inverse trig ratios to find missing angle measures:
sine-1, cos-1, tan-1,
Example 4
Find Angle Measures Using Inverse Trigonometric
Ratios
Use a calculator to find the measure of P to the nearest
tenth.
Example 4
Use a calculator to find the measure of D to the nearest
tenth.
A. 44.1°
B. 48.3°
C. 55.4°
D. 57.2°
Try it! Find each angle measure.
• Pg. 571 #4A and 4B
Example 5
Solve a Right Triangle
Solve the right triangle. Round side measures to the
nearest hundredth and angle measures to the nearest
degree.
Example 5
Solve the right triangle. Round side measures to the
nearest tenth and angle measures to the nearest degree.
A. mA = 36°, mB = 54°,
AB = 13.6
B. mA = 54°, mB = 36°,
AB = 13.6
C. mA = 36°, mB = 54°,
AB = 16.3
D. mA = 54°, mB = 36°,
AB = 16.3
Example 1
Angle of Elevation
CIRCUS ACTS At the circus, a person in the audience at
ground level watches the high-wire routine. A 5-foot-6inch tall acrobat is standing on a platform that is 25 feet
off the ground. How far is the audience member from
the base of the platform, if the angle of elevation from
the audience member’s line of sight to the top of the
acrobat is 27°?
Make a drawing.
Example 2
Angle of Depression
DISTANCE Maria is at the top of a cliff and sees a seal in
the water. If the cliff is 40 feet above the water and the
angle of depression is 52°, what is the horizontal
distance from the seal to the cliff, to the nearest foot?
Make a sketch of the situation.
Since
are parallel,
mBAC = mACD by the
Alternate Interior Angles
Theorem.
Example 1
DIVING At a diving competition, a 6-foot-tall diver stands
atop the 32-foot platform. The front edge of the platform
projects 5 feet beyond the ends of the pool. The pool itself
is 50 feet in length. A camera is set up at the opposite end
of the pool even with the pool’s edge. If the camera is
angled so that its line of sight extends to the top of the
diver’s head, what is the camera’s angle of elevation to the
nearest degree?
A. 37°
B. 35°
C. 40°
D. 50°
Example 2
Luisa is in a hot air balloon 30 feet above the ground. She
sees the landing spot at an angle of depression of 34.
What is the horizontal distance between the hot air
balloon and the landing spot to the nearest foot?
A. 19 ft
B. 20 ft
C. 44 ft
D. 58 ft