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
VikaD [51]
3 years ago
14

What is the length of the hypotenuse of the triangle below

Mathematics
2 answers:
Hatshy [7]3 years ago
4 0
One way to solve this is to use Pythagorean theorem: the square of one leg of triangle plus square of other leg of the triangle equals c the hypotenuse (longest side of triangle). You might see this as the formula a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.
In this case, the legs are 3√2 and the hypotenuse is h.
Using the formula:
(3√2)² + (3√2)² = h²
18 + 18 = h²
h = 6

The other way to do this is with trigonometric angles.
Remember cosine is adjacent over hypotenuse.
cos(45°) = (3√2) / h
h = (3√2) / cos(45°)
h = 6

mezya [45]3 years ago
3 0

The value hypotenuse of given triangle is \fbox{\bf 6 units}.

Further explanation:

Method 1:

Pythagoras theorem:

For a \triangle ABC, right angle at B following relation holds:

{\left({AC}\right)^2}={\left( {AB}\right)^2}+{\left( {BC}\right)^2}     ……(1)

Consider the given triangle as \triangle ABC shown below in Figure 1.

Substitute 3\sqrt 2  for AB, 3\sqrt 2 for BC and h for AC in equation (1).

\begin{aligned}{h^2}&={\left( {3\sqrt2}\right)^2}+{\left({3\sqrt2}\right)^2}\\{h^2}&=18+18\\{h^2}&=36\\h&=6\\\end{aligned}

Thus, the value hypotenuse of given triangle is \fbox{\bf 6 units}.

Method 2:

Consider the given triangle as \triangle ABC as shown below in Figure 1.

In right \triangle ABC, BC is base, AB is perpendicular and AC is hypotenuse.

sin is defined as the ratio of perpendicular to hypotenuse, cos is defined as the ratio of base to hypotenuse and tan is defined as the ratio of perpendicular to base. There exists three more ratios which are reciprocal of sin,cos and tan.

For \angle C, these ratios can be listed as shown below.

\begin{aligned}{\text{sinC=}}\frac{{AB}}{{AC}},\,{\text{\,\,\,\,\,\,\,\,cosecC=}}\frac{{AC}}{{AB}}\hfill\\{\text{cosC=}}\frac{{BC}}{{AC}},{\text{\,\,\,\,\,\,\,secC=}}\frac{{AC}}{{BC}}\hfill\\\tan C {\text{}}\frac{{AB}}{{BC}},\,\,\,\,\,\,\,\,\,\,\cot\,C{\text{=}}\frac{{BC}}{{AB}} \hfill\\\end{aligned}

Substitute 3\sqrt 2  for AB, h for AC and 45 for \angle C.

\begin{aligned}{\text{sin45=}}&\frac{{3\sqrt2}}{h}\hfill\\\frac{1}{{\sqrt2}}&=\frac{{3\sqrt 2 }}{h}\hfill\\h&=\left({3\sqrt2}\right)\left({\sqrt2}\right)\hfill\\h&=6\hfill\\\end{aligned}

Thus, the value hypotenuse of given triangle is \fbox{\bf 6 units}.

Learn more:  

1. Which rule describes the transformation? brainly.com/question/2992432  

2. Which undefined term is needed to define an angle? brainly.com/question/3717797  

3. Look at the figure, which trigonometric ratio should you use to find x? brainly.com/question/9880052  

Answer Details :

Grade: Senior School  

Subject: Mathematics  

Chapter: Triangle.

Keywords:

triangle ABC, sin, cos, tan, cot, sec, cosec, angle, Pythagoras theorem, hypotenuse, base, perpendicular, trigonometric ratio, similarity, ratio of sides, right triangle, similar triangle, ratio of sides, equal angles, square of hypotenuse, sum, square of legs, sum of square of legs, sum of angle of triangle, property of triangle, triangle ABC.  

You might be interested in
Fill in the blanks below in order to justify whether or not the mapping shown
MrRa [10]

Answer:

wheres the picture?

Step-by-step explanation:

6 0
3 years ago
Determine whether the graphs of y=-7x-4 and -y=7x+4 are parallel, perpendicular, coincident or none of these
horsena [70]

we are given

y=-7x-4

-y=7x+4

we can multiply -1 on both sides of second equation

-1*-y=-1(7x+4)

y=-7x-4

we can see that

both equations becomes same

so, they are coincident............Answer

5 0
3 years ago
Read 2 more answers
Factor the polynomial x(3x+5)-4(3x+5)
padilas [110]
<span>x(3x+5)-4(3x+5)
3x^2+5x-12x+20
3x^2-7x+20</span>
3 0
3 years ago
Read 2 more answers
Circle area of a radius of 3
Nat2105 [25]

Answer:

A=28.27

Step-by-step explanation:

8 0
3 years ago
HELP ASAP!!! You are going on a camping trip with you family for 3 days. You decide you need 5 batteries for you flashlights. At
ANTONII [103]

Answer:

15 batteries.

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • 85 POINT QUESTION, WILL MARK BRAINLIEST.
    7·2 answers
  • A bottle contains 568 millilitres of milk, jack pours out half a litre. How much milk is left
    15·1 answer
  • At a certain high school, 450 out of 500 seniors will graduate and half of the graduates will go to college. What percentage of
    14·1 answer
  • Classify the following triangle as acute,obtuse, or right
    8·2 answers
  • A ladder reaches the top of a 20 foot building. the ladder is 4.5 feet away from the building. how long is the ladder?
    5·1 answer
  • What is the main difference when finding an inverse and solving a square root equation?
    5·2 answers
  • Evaluate the expression shown below and write your answer as a fraction in simplest form.
    10·2 answers
  • What is 2/5 ×5/6 in simplist form
    10·2 answers
  • Which statement is true?
    10·1 answer
  • (1,5) (2,7)<br> How to find the equation of the line passing through the given points
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!