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3 years ago

Plz help- a through c

Mathematics

1 answer:

Sedbober [7]3 years ago

8 0

Answer:

a) find the unknowns

b) use the tangent to find the other leg; proceed as in (c)

c) use the arctangent to find the angle (if unknown); use the cosine and adjacent leg to find the hypotenuse. The other angle is the complement.

Step-by-step explanation:

a) "Solve a triangle" means "find the values of all the angles and side lengths." There are 6 measures in all. Three must be given, including at least one side (or hypotenuse) length, in order to solve the triangle.

b) We interpret "side length" to mean the length of one leg, not the hypotenuse. If the hypotenuse is given the procedure is slightly different.

The given side will either be adjacent to or opposite the given angle. If it is adjacent, the opposite side is found from ...

Opposite = Tan( )×Adjacent

If the given side is opposite the angle, the adjacent side is found from ...

Adjacent = Opposite/Tan( )

Now, you have both opposite and adjacent sides, and one angle. To find the remaining measures, use the procedures in part (c).

c) If neither angle is given, choose the longer side as the "adjacent" side and find the angle from ...

smaller acute angle = arctan(Opposite/Adjacent)

The other acute angle is the complement of the one you know.

Now, you have both acute angles, and both legs of the triangle.

Again, choosing the longer leg as "adjacent," use the cosine function to find the hypotenuse:

Hypotenuse = Adjacent/Cos( )

Of course, you can also find the hypotenuse using the Pythagorean theorem:

H = √(A² +O²)

_____

Examples:

b) given a side 4 and an opposite angle of 57°.

Using the formula above:

adjacent = 4/tan(57°) = 2.5976

angle adjacent to 4 = 90° -57° = 33°

hypotenuse = 4/cos(33°) = 4.7695

Angles: 33°, 57°, 90°; sides: 2.5976, 4, 4.7695.

c) given side lengths of 3 and 4

smaller acute angle = arctan(3/4) = 36.87°

larger acute angle = 90° -36.87° = 53.13°

hypotenuse = 4/cos(36.87°) = 5

Angles: 36.87°, 53.13°, 90°; sides: 3, 4, 5.

_____

Note that in all cases, the full calculator precision should be maintained for all intermediate values. No numbers should be rounded until their final presentation as the solution to the problem.

_____

Additional comment on this solution

For a given acute angle, you can also be given any of three sides: opposite, adjacent, or hypotenuse. To simplify our solution process here, we have assumed the hypotenuse is not a side given.

Basically, choose the relation in SOH CAH TOA that will have one unknown when you fill in the known values. Use that to find the unknown. Repeat until all are known, making use of the fact that acute angles are complementary, as needed. You can also use the Pythagorean theorem to find unknown sides when two are known.

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In the triangle, find x, y, u, v

Gwar [14]

Answer:

x = 9
y = 12
u = 24
v = 32

Step-by-step explanation:

Each of the triangles is similar, so we have ...

3/5 = (3+x)/20

x = 20(3/5) -3

x = 9

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y = 20(4/5) -4

y = 12

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v = 60(4/5) -4 -12

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3 years ago

Help with some math homework? The area of a triangle is 110 square inches. the height of the triangle is 8 less than 3 times its

Alenkasestr [34]

A = h x b; where A = area of a triangle; h = height of the triangle; b = base of the riangle;
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3 years ago

Please I really need help with this question

barxatty [35]

Answer:

Step-by-step explanation:

ABC and DEF are parallel lines. So, ∠ABE and ∠BED are co interior angles.

∠ABE + ∠BED = 180 {SUM OF CO INTERIOR ANGLE IS 180}

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∠ABE = 180 - 110.2

∠ABE = 69.8

Now, ABC is straight line

∠ABE + ∠EBG + ∠CBG = 180

69.8 + ∠EBG + 34.8 = 180

104.6 + ∠EBG = 180

∠EBG = 180 - 104.6

∠EBG = 75.4

Again, DEF is straight line

∠DEB + ∠BEG + ∠GEF = 180

110.2 + ∠BEG + 25.6 = 180

∠BEG + 135.8 = 180

∠BEG = 180 - 135.8

∠BEG = 44.2

In triangle BEG,

∠BEG + x + ∠EBG = 180 { sum of all angles of triangle is 180}

44.2 + x + 75.4 = 180

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3 years ago

Seth buys last year's best-selling novel, in hardcover, for $17.85 $⁢17.85 . This is with a 15% 15% discount from the original p

Troyanec [42]

$21.00

let the original price = 100%

then the discount price = 100 - 15 = 85%

divide $17.85 by 85 to obtain 1% then multiply by 100 to obtain original price.

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3 years ago

Read 2 more answers

A store owner uses a selling price of 125% of the cost of an item. If a pair of jeans has a sales price of $52.50, what cost doe

IgorC [24]

Answer:

The cost store owner pay for the pair of jeans is $42.

Step-by-step explanation:

Given:

A store owner uses a selling price of 125% of the cost of an item.

If a pair of jeans has a sales price of $52.50.

Now, to find the cost price of the store owner pay for the pair of jeans.

Let the cost price of jeans be $x.$

Sell price of jeans = $\$52.50.$

Now, to get the cost price of store owner pay for the pair of jeans:

As given the store owner uses a selling price of 125% of the cost of an item.

According to question:

$125\%\ of\ x=52.50$

$\frac{125}{100} \times x=52.50$

$1.25x=52.50$

Dividing both sides by 1.25 we get:

$x=42.$

The cost price of jeans = $42.

Therefore, the cost store owner pay for the pair of jeans is $42.

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2 years ago