Honors Analysis
Section 6.6
Chapter 6 Review – Right Triangles
1.)
2.)
3.) Determine the area of an equilateral
triangle with 5 cm sides. Write your
answer in simplified radical form.
4.) Humphrey skied 2 km north, 2 km west, 1 km north, and 2 km
west. How far was he from his starting point?
5.) If the altitude of an equilateral triangle
is 8√3 cm, what is the perimeter?
6.) A rhombus has diagonals of length 12 and 16. What is the
perimeter?
7.) What is the length of the diagonal of
a 6 by 7 by 8 rectangular prism?
8.) A cube has a diagonal measuring 7√6 cm. How long are the
sides?
9.) A triangle has side lengths of 5, 7, and 8
cm. Is the triangle acute, obtuse, or right?
How do you know?
10.) Solve for x:
11.)
12.)
Answer the following questions using the diagram below:
13. A) cos A =
D) 𝑚∠𝐶 =
B) sin A =
C) tan C =
14.) Rationalize the denominator:
√2
4−√5
15.) A line with a slope of 2/7 intersects the x-axis at what
acute angle measure? Round to the nearest tenth of a degree.
Use a 45-45-90 and a 30-60-90 triangle to calculate each value. Write your answer as a simplified fraction. DO NOT give
the approximate decimal value from your calculator!
16. A) sin 30º
B) cos 30º
C) tan 60º
D) tan 45º
17.) Determine the area of a regular hexagon
with 20 cm sides. Write your answer in simplified
radical form.
18.) Calculate the area of a regular decagon with 6 in
sides. Round to the nearest hundredth.
.
19.) Determine the area of a circle inscribed in an
equilateral triangle with 24 cm sides.
20. Each side of the base of a square pyramid
measures 14 in and the altitude is 24 in.
A) What is the lateral surface area? Total area?
B) What is the volume?
21.)
22.)
23.) A ship is on the surface of the water and its
radar detects a submarine at a distance of 238 feet,
at an angle of depression of 23º. How deep
underwater is the submarine?
24.) A cube has a diagonal measuring 8√6 cm.
How long are its sides?