solving right triangles - effingham county schools …...solving right triangles ex 3: find the...
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WarmUp Find the sin θ, cos θ, and tan θ.
25
60
65 θ
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How do you solve right triangles?
Unit 3 Day 6
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San Francisco
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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.
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5cos
13 1 1cos ( ) co
5cos
13s
67.4
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Calculating Angle Measures from
Trigonometric Ratios
Use your calculator to find each angle measure to the nearest tenth of a degree.
A. cos-1(0.87) B. sin-1(0.85) C. tan-1(0.71)
cos-1(0.87) 29.5° sin-1(0.85) 58.2° tan-1(0.71) 35.4°
Example 1
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Inverse trig functions:
Ex 2: Use a calculator to approximate the
measure of the acute angle. Round to the
nearest tenth.
26.6° 20.5° 50.2°
1tan (0.5)m A 1sin (0.35)m A
1cos (0.64)m A
a. tan A = 0.5 b. sin A = 0.35 c. cos A = 0.64
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Solving Right Triangles
Ex 3: Find the unknown measures. Round lengths to the nearest
hundredth and angle measures to the nearest degree.
Since the acute angles of a right triangle are complementary, mT 90° – 29° 61°.
RT2 = RS2 + ST2
(5.7)2 = 52 + ST2
Since the acute angles of a right triangle are complementary, mT 90° – 29° 61°.
, so ST = 5.7 sinR.
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Ex 4: Solve the right triangle. Round decimals the nearest tenth.
3
2
90
AB
BC
AC
m A
m B
m C
Use Pythagorean Theorem to find c… 2 2 32 3
3.6
c
c
3.6 Use an inverse trig function to
find a missing acute angle…
1 3tan ( ) 56.3
2m A
Use Triangle Sum Theorem to
find the other acute angle…
90 56.3 33.7m B
56.3°
33.7°
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Ex 5: You are hiking up a mountain peak. You begin hiking at a trailhead whose elevation is about 9400 ft. The trail ends near the summit at 14,255 ft. The horizontal distance between these two points is about 17,625 ft. Estimate the angle of elevation from the trailhead to the summit.
opposite side: 14,255ft-9,400ft 4,85= 5 ft
4855tan
17625A
1 4855tan ( )
17625
15.4
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Ex 6: A monster truck drives off a ramp in order to jump onto a row
of cars. The ramp has a height of 14 feet and a horizontal length of 26 feet. What is the angle θ of the ramp? Round your answer to the nearest integer, if necessary.
14 ft
26 ft
14tan
26 1 14
tan ( )26
28.3
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Homework:
Page 331-332 #7-13, 15, 35
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Ex 3: Solve the right triangle. Round to the nearest tenth.
53
90
30
m Q
m R
m P
PQ
PR
QR
37°
18.1
24.0
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Example 2:
a.
b.
17sin
240A 1 17
sin ( )240
4.1 Convert 20 ft to in
To minimize horizontal distance use the greatest possible ramp angle
8tan(4.76 )
x
96.1 in.x