Transcript Unit 0 4.1 Solving Right Triangles

Unit 0 4.1 Solving Right
Triangles
OBJ: SWBAT solve triangles using the
six trigonometric ratios.
HW: p 259 (29,33, 37, 41)
Solving a right triangle
• Every right triangle has one right angle,
two acute angles, one hypotenuse and two
legs. To solve a right triangle, means to
determine the measures of all six (6) parts.
You can solve a right triangle if the
following one of the two situations exist:
– Two side lengths
– One side length and one acute angle
measure
WRITE THIS DOWN!!!
• In general, for an acute angle A:
– If sin A = x, then sin-1 x = mA
– If cos A = y, then cos-1 y = mA
– If tan A = z, then tan-1 z = mA
The expression sin-1 x is read as “the inverse sine
of x.”
• On your calculator, this means you will be
punching the 2nd function prior to doing the
calculation. This is to find the degree of the
angle.
Ex 1) Solve the right triangle. Round to the
nearest tenth.
g
J
H
25°
13
sin 25o 
13sin 25o 
h
13
h
13
13
5.5 ≈ h
cos 25o 
13cos 25o 
g
13
g
13
13
11.8 ≈ g
mG  90o  25o
mG  65o
h
G
Ex 2) Solve the right triangle. Round to the
C
nearest tenth.
3
B
c2
=
a2
+
b2
c2 = 32 + 22
c2 = 9 + 4
c2 = 13
c = √13
c ≈ 3.6
tan A 
3
2
3
mA  tan 1  
2
mA  56.3o
2
c
mB  90o  56.3o
mB  33.7o
A
Using Right Triangles in Real Life
• Space Shuttle:
During its approach to
Earth, the space shuttle’s
glide angle changes.
Ex 3a)
Glide  = x°
altitude
15.7
miles
When the shuttle’s altitude
is about 15.7 miles, its
horizontal distance to the
runway is about 59 miles.
What is its glide angle?
Round your answer to the
nearest tenth.
distance to runway
59 miles
tan x o 
15.7
59
 15.7 
m x  tan 1 

 59 
m x  14.9o
Ex 3b)
Glide  = 19°
altitude
h
When the space shuttle is 5
miles from the runway, its glide
angle is about 19°.
Find the shuttle’s altitude at
this point in its descent.
Round your answer to the
nearest tenth.
distance to runway
5 miles
h
tan19 
5
o
5 tan19o 
h
5
5
1.7 miles ≈ h