Transcript EXAMPLE 5 Find leg lengths using an angle of elevation SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14

EXAMPLE 5
Find leg lengths using an angle of elevation
SKATEBOARD RAMP
You want to build a skateboard ramp with a length of
14 feet and an angle of elevation of 26°. You need to
find the height and length of the base of the ramp.
EXAMPLE 5
Find leg lengths using an angle of elevation
SOLUTION
STEP 1
Find the height.
opp.
sin 26o =
hyp.
x
14
sin 26o =
14 sin 26o = x
6.1
ANSWER
x
Write ratio for sine of 26o.
Substitute.
Multiply each side by 14.
Use a calculator to simplify.
The height is about 6.1 feet.
EXAMPLE 5
STEP 2
Find leg lengths using an angle of elevation
Find the length of the base.
adj.
cos 26o =
hyp.
y
14
cos 26o =
14 cos 26o = y
12.6
ANSWER
y
Write ratio for cosine of 26o.
Substitute.
Multiply each side by 14.
Use a calculator to simplify.
The length of the base is about 12.6 feet.
EXAMPLE 6 Use a special right triangle to find a sine and cosine
Use a special right triangle to find the sine and cosine
of a 60o angle.
SOLUTION
Use the 30o - 60o - 90o Triangle Theorem to draw a right
triangle with side lengths of 1, 3 , and 2. Then set up
sine and cosine ratios for the 60o angle.
o
sin 60
opp.
=
=
hyp.
3
2
adj.
=
hyp.
1
2
cos 60o =
0.08660
= 0.5000
GUIDED PRACTICE
for Examples 5 and 6
7. WHAT IF?
In Example 5, suppose the angle of elevation is 35o.
What is the new height and base length of the ramp?
ANSWER
about 8 feet, about 11.5 ft
8. Use a special right triangle to find the sine and
cosine of a 30o angle.
ANSWER
1 ,
2
3
2