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Math Problems
Grade 6
Find missing angles in special triangles
Use the
45
45
45
−
45
-45
−
45
−
90
-90
−
90
pattern to find both missing side lengths of each right triangle:
\newline
2
2
2
)
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In a right triangle, one angle measures
x
∘
x^\circ
x
∘
, where
\newline
sin
x
∘
=
4
5
\sin x^\circ = \frac{4}{5}
sin
x
∘
=
5
4
. What is
cos
(
9
0
∘
−
x
∘
)
\cos(90^\circ - x^\circ)
cos
(
9
0
∘
−
x
∘
)
?
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For the following right triangle, find the side length
x
x
x
. Round your answer to the nearest hundredth.
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ne surface area of the trianguiar prism. The base of the prism is an isosceles triangle. The surtace area is
□
cm
2
\square \, \text{cm}^{2}
□
cm
2
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ne surtace area of the triangular prism. The base of the prism is an isosceles triangle.
\newline
The surtace area is
□
\square
□
c
m
2
\mathrm{cm}^{2}
cm
2
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Triangle RST is similar to triangle RVW.
\newline
What is the value of
d
d
d
in centimeters?
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Below is a right triangle and a rectangle. Find the perimeter of the figure.
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A right triangle has sides of
6
c
m
,
8
c
m
6 \mathrm{~cm}, 8 \mathrm{~cm}
6
cm
,
8
cm
, and
10
c
m
10 \mathrm{~cm}
10
cm
. Determine the measure of the smallest angle,
θ
\theta
θ
.
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Triangles
\newline
6
6
6
\newline
In triangle
A
B
C
A B C
A
BC
, the length of side
A
B
A B
A
B
is
10
10
10
inches and the length of side
B
C
B C
BC
is
17
17
17
inches. Which of the following could be the length of side
A
C
A C
A
C
?
\newline
A.
5
5
5
inches
\newline
B.
29
29
29
inches
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What is the part of a line that contains two points and all other points between them?
\newline
line segment
\newline
bisector
\newline
arc
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The area of a triangle is
6
6
6
. Two of the side lengths are
7
7
7
.
1
1
1
and
5
5
5
.
3
3
3
and the included angle is acute. Find the measure of the included angle, to the nearest tenth of a degree.
\newline
Answer:
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The area of a triangle is
3
3
3
. Two of the side lengths are
1
1
1
.
8
8
8
and
4
4
4
.
8
8
8
and the included angle is acute. Find the measure of the included angle, to the nearest tenth of a degree.
\newline
Answer:
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Find the area of triangle with base
5
cm
5\,\text{cm}
5
cm
and height
7
cm
7\,\text{cm}
7
cm
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(
1
1
1
) An isosceles right triangle has an area
8
cm
2
8\text{cm}^2
8
cm
2
. The length of its hypotenuse is
\newline
cm
16
\text{cm}\sqrt{16}
cm
16
\newline
cm
48
\text{cm}\sqrt{48}
cm
48
\newline
cm
32
\text{cm}\sqrt{32}
cm
32
\newline
24
cm
\sqrt{24}\text{cm}
24
cm
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3
3
3
. Given right triangle
G
H
I
G H I
G
H
I
, with right angle at
H
,
G
H
=
12.2
H, G H=12.2
H
,
G
H
=
12.2
, and
m
∠
G
=
2
8
∘
m \angle G=28^{\circ}
m
∠
G
=
2
8
∘
, find the measures of the remaining sides to the nearest tenth.
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