Free Printable EOM 2 pt 2

1.

Consider the two triangles. Each row of the table shows the lengths of the legs and hypotenuses of these triangles. Drag and drop the missing lengths, in simplest radical form, into the correct box.

a)

5

b)

5

c)

$5\ \sqrt[]{3}$

d)

$10\ \sqrt[]{2}$

e)

$5\ \sqrt[]{2}$

f)

10

g)

2.5

h)

20

i)

$10\ \sqrt[]{3}$

1

2

3

4

1)

2)

3)

4)

2.

If x and y are the measures of complementary angles in a right triangle such that cos y = $\frac{3\sqrt{39}}{20}$ and tan x = $\frac{3\sqrt{39}}{7}$ , label the sides of the right triangle in the diagram below with possible side lengths.

Drag values to each side of the triangle to create your answer.

a)

$3\ \sqrt[]{39}$

b)

3

c)

$\sqrt[]{39}$

d)

20

e)

7

f)

39

1

2

3

1)

2)

3)

3.

A 103-foot wire is used to support a utility tower. It runs from the tower to the ground and forms a 24° angle with the ground. Use the values in the table to calculate the following distances. Round your answers to the nearest tenth.

The distance from the base of the utility tower to the location where the wire is attached to the ground is

(a)

4.

A 103-foot wire is used to support a utility tower. It runs from the tower to the ground and forms a 24° angle with the ground. Use the values in the table to calculate the following distances. Round your answers to the nearest tenth.

The wire attaches to the utility tower at a height of

(a)

5.

A ladder is leaning against a building. The ladder forms an angle of 77° with the ground. The distance from the base of the ladder to the base of the building is 8 feet.

How high on the building does the ladder make contact? Round your answer to the nearest hundredth.

Values in the table are rounded to the ten-thousandths place.

(a)

6.

Consider a right triangle with acute angle of measure θ and cos θ = $\frac{4}{7}$ .

Use the Pythagorean identity to write an equation that can be used to find sin.

7.

Consider a right triangle with acute angle of measure θ and cos θ = $\frac{4}{7}$ .

Then find the value of sin θ in simplest radical form.

8.

Consider a right triangle with acute angle of measure θ and cos θ = $\frac{4}{7}$ .

Which of the following expressions are equivalent to tan θ?

a)

$\frac{7}{4}$

b)

$\frac{\sqrt[]{33}}{4}$

c)

$\frac{4\ \sqrt[]{33}}{33}$

d)

$\ \frac{7\ \sqrt[]{33}}{33}$

9.

Remy stands on a dock at the edge of a lake represented by point C. Points A and B represent two buoys anchored in the lake. Remy plans to swim from C to A, then to B, and then back to C. The shortest distance from Remy to the swim route AB is 60 meters and is measured from C to D.

What is the total distance, in meters, that Remy will swim?

Round your answer to the nearest whole number.

(a)

EOM 2 pt 2

Total questions: 9

Worksheet time: 2hrs 15mins

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