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
14

Consider the case of a triangle with sides 5, 12, and the angle between them 90°.

Mathematics
1 answer:
Daniel [21]3 years ago
3 0

Answer:

a) Applying Pithagoras Theorem

b) Trigonometric relations

c) No we can not

d) No we can not

e) See step-by-step explanation

f) See step-by-step-explanation

Step-by-step explanation:

a) The easiest method for calculating the missing side is applying Pithagoras Theorem

c²  =  a²  +  b²

c²  =  (5)²  +  (12)²      ⇒  c²  = 25 + 144    ⇒ c²  =  169    ⇒  c  = 13

b) The easiest method to find the missing angles, is to calculate the sin∠ and then look for arcsin fuction in tables.

sin ∠α = 5/13    sin ∠α = 0.3846    ⇒      arcsin (0.3846 )   α  = 23⁰

Now we can either get the other angle subtracting 180 - 90 - 23 = 67⁰

Or calculating sinβ = 12 /13    sinβ = 0.9230  arcsin(0.9230)   β = 67⁰

c) The law of cosines should not be applied to right triangles, in fact for instance in our particular case we have:

Question a)

c²  = a² + b² - 2*a*b*cos90⁰   (law of cosines ) but cos 90⁰ = 0

then c²  = a² + b² which is the expression for theorem of Pithagoras

In case you look for calculating the missing angles

c²  = a²  +  b²  - 2*5*13*cos α

169 = 25  +  144 - 2*5*13* cos α

As you can see 169 - 25 - 144 = 0

Then we can not  apply law of cosine in right triangles, we shoul apply trigonometric relations and Pithagoras theorem, and as we saw you can get the expression of Pithagoras theorem from cosine law

c²  =  a²  +  b²  - 2*a*b*cos∠90°    cos ∠ 90°  = 0

Then     c²  =  a²  +  b²

You might be interested in
a model railroad kit contains curved tracks and straight tracks . Given that 35 % of the tracks are curved , what fraction of th
Pani-rosa [81]
Since 35% of the tracks are curved, 65% of the tracks must be straight.

65% = 65/100 = 13/20
4 0
3 years ago
Plzzzz help asap lost ten u gain it asap
faltersainse [42]
Your unit cost will be $0.11 :) 
7 0
3 years ago
10x+2 = 3x + 30 Find x (please)
Ganezh [65]
Answer: x=4

10x-3x=30-2
7x=28
X=4
7 0
3 years ago
Find the area of the triangle
kupik [55]
Area = 1/2 * base * height 
 = 1/2 * 20 * 6
 = 1/2 * 120
 = 60 ft^2
6 0
3 years ago
1 point
77julia77 [94]

Answer:

A negative integer

Step-by-step explanation:

3x - 2(5x+12) - 32 = 0

3x - 10x - 24 - 32 = 0

-7x -56 = 0

-7x = 56, x = -8

y = 5(-8) + 12, y = -28

6 0
2 years ago
Other questions:
  • Plz help I just need numbers
    9·1 answer
  • A malapropism occurs when two people use the same word to mean two different things
    6·1 answer
  • From 6 cards bearing the letters a, b, c, d, e, and f, two cards are drawn. Find the probability that at least one of the cards
    9·2 answers
  • If y varies directly with x, and x=21 and y=14, what is the equation that represents this variation?
    9·1 answer
  • What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x? 1. The distributive property: 4x – 12 + 4 < 10
    7·2 answers
  • Will give Brainliest! if right!
    5·2 answers
  • 1) Suppose you buy a laptop costing $1850 at a store charging 12% add-on interest, and you make a $500 down payment.
    15·1 answer
  • Maureen spent $34.05 on 3 fancy pens. How much did each pen cost
    7·2 answers
  • I nee d help asap!!!
    15·2 answers
  • Solve the attached question.<br><br>No spam allowed!​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!