Download 7.5 - Solving Right Triangles

A grain auger lifts grain from the
ground to the top of a silo. The
greatest angle of elevation that is
possible for the auger is 35o. The
auger is 18m long.
18 m
What is the maximum height
that the auger can reach?
h
35o
h
18 m
35o
First, draw a diagram.
From the angle, we are dealing
with the opposite side (h) and the
hypotenuse (18 m).
We can use sine to find h
=
ℎ = 18 × sin(35o)
ℎ ≅ 10
sin(35o)
h
18 m
35o
=
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
ℎ
18
Therefore, the maximum height
that the auger can reach is about
10 meters.
55 mm
15o
p
Determine the length of p.
We are dealing with the adjacent
side (55 mm) and the hypotenuse
(p) so we can use cosine.
cos(15o) =
𝑝=
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
=
55
𝑝
55
cos(15o)
𝑝 ≅ 57
Therefore, the length of p is about 57 mm long.
Noah is flying a kite and has released
25m of string. His sister is standing
8m way, directly below the kite. What
is the angle of elevation of the string?
Hypotenuse
25 m
We know adjacent and hypotenuse so
we can use cosine:
opposite
cos𝜃 =
𝜃
𝜃=
8m
(adjacent)
Noah
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
cos −1
𝜃 ≅ 71o
Sister
=
8
25
8
25
Therefore, the angle of
elevation of the string is
about 71o.
Trigonometric ratios can be used to calculate unknown side
lengths and unknown angle measures in a right triangle
The ratio you use depends on the information given and the
quantity you need to calculate