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2 years ago

I will give lots of points please help me

Mathematics

2 answers:

k0ka [10]2 years ago

5 0

Answer:

Part A: 6

Part B: 6√3

Step-by-step explanation:

Part A:

Since one angle measures 30°, and another angle is a right angle measuring 90°, the third angle measures 60°.

In a 30-60-90 the short leg is half of the hypotenuse.

YX = 12/2 = 6

Part B:

Method 1:

In a 30-60-90 triangle, the length of the long leg is √3 times the length of the short leg.

YZ = 6√3

Method 2:

Use the Pythagorean theorem.

a² + b² = c²

6² + (YZ)² = 12²

(YZ)² = 108

YZ = √(108)

YZ = √(36 × 3)

YZ = 6√3

strojnjashka [21]2 years ago

4 0

sin30=XY/XZ
1/2=XY/12
XY=6

Cos30=YZ/XZ
√3/2=YZ/12
YZ=6√3

Another way is using Pythagorean theorem

YZ²=XZ²-XY²

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Answer:

used ckmgtdctstrrerwy45ykehrakut

7 0

2 years ago

What equals 210 im trying to find this answer out for hours and hours

ale4655 [162]

21*10=210 30*7=210 42*5=210 14*15=210

3 0

3 years ago

the ratio of peters money to henrys money is 4 : 3 there at first. after perter spent 12 dollars they had an equal amount of mon

MatroZZZ [7]

Using a system of equations, it is found that Peter had $48 at first.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Variable x: Peter's money.

Variable y: Henry's money.

The ratio of peters money to henrys money is 4 : 3, hence:

$\frac{x}{y} = \frac{4}{3}$

After Peter spent $12, they had the same amount, hence:

y = x - 12.

Then, replacing in the ratio:

$\frac{x}{y} = \frac{4}{3}$

$\frac{x}{x - 12} = \frac{4}{3}$

4(x - 12) = 3x

x = 48.

More can be learned about a system of equations at brainly.com/question/24342899

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4 0

2 years ago

A right prism has a base that is an equilateral triangle. The height of the prism is equal to the height of the base. If the vol

Romashka [77]

<u>Answer:</u>

Lengths of the sides (there are 3 sides in an equilateral triangle) of the base of prism is <u>5.72cm </u>each.

<u>Step-by-step explanation:</u>

As the base of triangular prism is equilateral:

∴ Area of base = (√ 3 / 4)× (side)²

According to question:

height of prism = height (side) of base

Volume of prism = 81 cm³,

∴ Volume of prism = Area of base x height

⇒ 81 cm³ = (√ 3 / 4)× (side)² × height ∵ side = height

⇒ 81 cm³ = (√ 3 / 4)× (side)³

⇒ 81 × (4/√3) cm³ = side³

⇒ ∛(81 × (4/√3) cm = side

⇒ side = <u>5.72cm</u>

6 0

3 years ago

A ramp is 35 ft long rises to a platform. The bottom is 15 ft from the foot of the ramp. Find x, the angle of elevation of the r

sineoko [7]

Answer:

The angle of elevation of the ramp is 64.60°

Step-by-step explanation:

Given;

length of the ramp, L = 35 ft

distance of the platform to the foot of the ramp, d = 15 ft

The length of the ramp forms the hypotenuse side of this right angled triangle;

The angle of elevation of the ramp is in angle between the hypotenuse and adjacent side of the triangle.

Cos x = adjacent / hypotenuse

Cos x = 15 / 35

Cos x = 0.4286

x = Cos⁻¹ (0.4286)

x = 64.62

x = 64.60°

Therefore, the angle of elevation of the ramp is 64.60°

4 0

3 years ago