1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
yulyashka [42]
3 years ago
11

The hypotenuse and one of the legs of a right triangle form an angle that has a cosine of 2 2 . what is the measure of the angle

?
a.30 degrees
b.45 degrees
c.60 degrees
d.90 degrees
Mathematics
1 answer:
creativ13 [48]3 years ago
7 0
The correct question is
The hypotenuse and one of the legs of a right triangle form an angle that has a cosine of √<span>2/2 . 
What is the measure of the angle? 

Let
</span>∅--------> the angle
cos ∅=√2/2<span>
cos </span>∅=[distance of one of the leg/hypotenuse]
[distance of one of the leg/hypotenuse]=√2/2

<span>I could say that
</span>distance of one of the leg=√2
and 
hypotenuse=2
so
<span>applying the Pythagorean theorem
</span>c=hypotenuse=2
a=√2
b=?
c²=a²+b²-------> b²=c²-a²------> b²=2²-(√2)²-----> b²=2-----> b=√2

therefore
if a=b
then 
the angle ∅=45°

the answer is the option
<span>b.45 degrees</span>
You might be interested in
Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D
Ivahew [28]
Check the picture below.

\bf \textit{Law of Cosines}\\ \quad \\&#10;c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies &#10;c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}&#10;\\\\\\&#10;\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\&#10;-------------------------------\\\\&#10;\begin{cases}&#10;d=10\\&#10;e=18\\&#10;f=22&#10;\end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D

\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D

7 0
3 years ago
The graph of a quadratic function has roots at -3 and -7 and a vertex at (-5, 4). What is the equation of the function in vertex
melomori [17]

Answer:

y = -(x + 5)² + 4

Step-by-step explanation:

The roots are -3 and -7, so:

y = a (x + 3) (x + 7)

Distribute and complete the square:

y = a (x² + 10x + 21)

y = a (x² + 10x + 25 − 4)

y = a (x² + 10x + 25) − 4a

y = a (x + 5)² − 4a

The vertex is (-5, 4), so a = -1.

y = -(x + 5)² + 4

3 0
3 years ago
N - 4 = 3n + 6<br> what number does n represent?
pav-90 [236]

Answer:

n = -5

Step-by-step explanation:

n - 4 = 3n + 6

n = 3n + 10

-2n = 10

n = -5

7 0
3 years ago
Read 2 more answers
Art Club Flyer
Finger [1]

The area of Erin's circle to the nearest hundredth is 50.24 in².

<h3>What is the area of the circle?
</h3>

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

  • π = pi = 3.14
  • R = radius

3.14 X 4²

(3.14) (4) (4) = 50.24 in²

To learn more about the area of a circle, please check: brainly.com/question/14351152

#SPJ1

8 0
1 year ago
Read 2 more answers
A lawn sprinkler spins in a circle. The sprinkler covers a radius of 12 feet. Which choice is the closest to the area of lawn th
Veronika [31]

You would do pi x r squared. r=12, and 12 squared is 144. pi (3.14) times 144 equals 452.16!

3 0
2 years ago
Other questions:
  • Describe the relationship between n and 4 that will make the value of the expression 7x n/4 greater than 7
    5·1 answer
  • A spherical balloon currently has a radius of 19cm. If the radius is still growing at a rate of 5cm or minute, at what rate is a
    11·1 answer
  • 9. The scale on a city map is 3/4 inch
    9·1 answer
  • The mean height of a group of students is 1.65 meter. Explain what this means.
    9·1 answer
  • Given: Circumscribed polygon ABCD AB=21, BC=24, CD=30 Find: AD AD = ____ units
    14·1 answer
  • Find the rate of change if this table explain how you calculated it.
    12·1 answer
  • Find the area of the trapezium​
    10·2 answers
  • I need help with this question <br><br>Help needed!!!!!!
    8·1 answer
  • Please help!!! .&gt; ^ &lt;.`
    11·1 answer
  • Write the equation of the line that is parallel to
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!