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
Mashcka [7]
3 years ago
13

Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C o

nly. You will need to use both Soh-Cah-Toa and the Pythagorean Theorem to solve for side AB.

Mathematics
1 answer:
Brrunno [24]3 years ago
6 0

Answer:

AB = \sqrt{a^2 + b^2-2abCos\ C}

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

Sin\ C = \frac{h}{a}

Make h the subject:

h = aSin\ C

Also, in BOC (Using Pythagoras)

a^2 = h^2 + x^2

Make x^2 the subject

x^2 = a^2 - h^2

Substitute aSin\ C for h

x^2 = a^2 - h^2 becomes

x^2 = a^2 - (aSin\ C)^2

x^2 = a^2 - a^2Sin^2\ C

Factorize

x^2 = a^2 (1 - Sin^2\ C)

In trigonometry:

Cos^2C = 1-Sin^2C

So, we have that:

x^2 = a^2 Cos^2\ C

Take square roots of both sides

x= aCos\ C

In triangle BOA, applying Pythagoras theorem, we have that:

AB^2 = h^2 + (b-x)^2

Open bracket

AB^2 = h^2 + b^2-2bx+x^2

Substitute x= aCos\ C and h = aSin\ C in AB^2 = h^2 + b^2-2bx+x^2

AB^2 = h^2 + b^2-2bx+x^2

AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2

Open Bracket

AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C

Reorder

AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C

Factorize:

AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C

In trigonometry:

Sin^2C + Cos^2 = 1

So, we have that:

AB^2 = a^2 * 1 + b^2-2abCos\ C

AB^2 = a^2 + b^2-2abCos\ C

Take square roots of both sides

AB = \sqrt{a^2 + b^2-2abCos\ C}

You might be interested in
Need help ASAP wleoeoowowoww
topjm [15]

Answer:

according to coordinates the answer to that question should be 4,-4

3 0
3 years ago
Show all work to multiply (3+ /(-16))(6-/(-64))
Reil [10]

Answer:

=50

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Answer the following question regarding the table below. 40 41 43 44 47 47 49 40 42 43 45 47 48 49 40 42 44 45 47 48 49 41 42 44
Stels [109]
Hello there, and thank you for posting your question here on brainly.

The smallest number out of the bunch is 40.

Hope this helps! 
4 0
3 years ago
Laura invests $2500 in one account and $1500 in an account paying 2 % higher interest. At the end of one year she had earned $11
Crank

Answer:

$2500 - 2%

$1500 - 4%

Step-by-step explanation:

Say the interest for the $2500 is x, so the interest for the $1500 is x+0.02.

As an equation, they would look like this:

2500x+1500(x+0.02)=110

Now solve

2500+1500x+30=110

4000x=80

x=0.02

That means the interest for the $2500 is 0.02, or 2%, and the interest for the $1500 is 0.04, or 4%.

6 0
3 years ago
Help pls will mark BRAINLY
Daniel [21]

Answer:

place your dots on the grid

Step-by-step explanation:

for example r would beeee uhm 3 y x 2

6 0
3 years ago
Other questions:
  • What is the value of (–7 + 3i) – (2 – 6i)
    15·1 answer
  • If a rectangle is quadrilateral with four right angles then what is the sum of its interior angles?
    14·1 answer
  • Superman and Spider-Man take turns in saving the world in the ratio of 4:3. There are 42 disastrous events , how many times do t
    9·1 answer
  • 14 inches to 2 yards
    12·2 answers
  • How to calculate the critical value of z distribution ?
    9·1 answer
  • If 3x+2=6 what is the value of x
    7·1 answer
  • Here is a system of equations.
    9·2 answers
  • Help me please please!!!!!!!!
    15·2 answers
  • (Elimination Strategies) Which of these strategies would eliminate a variable in the system of equations? x - 2y = 115x + 3y = -
    14·1 answer
  • What is the positionof C on the number line and how can i write the answer as a fraction or mixed number
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!