Please help me with this

A bike ramp is shown in the figure. What is theta, the bike ramp's angle of elevation? Round your answer to the nearest degree.

AysviL [449]

Answer:

Ф = 14° ⇒ to the nearest degree

Step-by-step explanation:

* Lets revise the trigonometry functions

- Assume that we have a right triangle ABC

∵ m∠B = 90°

∴ AC is the hypotenuse ⇒ opposite to the right angle

∴ AB and BC are the legs of the right angles

- Let angle ACB called Ф

∵ sinФ = opposite/hypotenuse

∴ sinФ = AB/AC

∵ cosФ = adjacent/hypotenuse

∴ cosФ = BC/AC

∵ tanФ = opposite/adjacent

∴ tanФ = AB/BC

* Now lets solve the problem

- We will consider the bike ramp is the ΔABC

∵ AB = 1.5 feet

∵ ∠ACB is Ф

∵ The length of the ramp is the hypotenuse

∴ AC = 6 feet

- W have the length of the opposite to Ф and the hypotenuse

∴ We will chose the sin function

∵ sinФ = AB/AC

∴ sinФ = 1.5/6 ⇒ use the inverse of sin to find Ф

∴ Ф = sin^-1 (1.5/6) = 14.47 ≅ 14° ⇒ to the nearest degree

3 0

2 years ago

Read 2 more answers

You are making snap bags, you want each bag to have the same combination you have 75 carrots and 40 celery sticks and you want t

makkiz [27]

Answer:

5 Bags

Step-by-step explanation:

There are 75 carrots and 40 celery sticks.

If we want each bag to have the same combination, the greatest number of bags we can make is determined by the Greatest common divisor of the two numbers.

To find the Greatest common divisor of 70 and 40

Step 1: Express each number as a product of its prime factors

40=2 X 2 X 2 X 5
75=3 X 5 X 5

Step 2: Pick each pair of common factors.

40=2 X 2 X 2 X 5
75=3 X 5 X 5

The only factor common to both pairs is 5.

Therefore, the Greatest common divisor of 70 and 40 is 5.

The greatest number of bags that can be made is 5.

4 0

2 years ago

Kendra just bought a new house and needs to buy new sod for her backyard. If the dimensions of her yard are 24.6 feet by 14.8 fe

Serhud [2]

Given:

Dimensions of Kendra's yard are 24.6 feet by 14.8 feet.

To find:

The area of her yard.

Solution:

Let as consider,

Length of yard = 24.6 ft

Width of yard = 14.8 ft

We know that,

Area of a rectangle = Length × Width

Using the above formula, we get the area of her yard.

$Area=24.6\times 14.8$

$Area=364.08$

Area of her yard is 364.08 ft² and without including the units ft², we get 364.08.

Therefore, the area of her yard is 364.08.

6 0

2 years ago

11th grade geometry:

Aliun [14]

Answer:

The perimeter is 72 units and the area is 149 square units.

Step-by-step explanation:

$\triangle SBA$ has coordinates $S(15,-8),B(-2,21)$ and $A(0,0)$

Using the distance formula.........

Length of side $SB = \sqrt{(15+2)^2+(-8-21)^2}= \sqrt{17^2+(-29)^2}= \sqrt{1130}$

Length of side $BA= \sqrt{(-2)^2+(21)^2}= \sqrt{445}$

Length of side $AS =\sqrt{(15)^2+(-8)^2}=\sqrt{289}=17$

So, the perimeter of the triangle will be: $(SB+BA+AS)= \sqrt{1130}+ \sqrt{445}+17 =71.71... \approx 72$ units. (Rounded to the nearest unit)

The height of the triangle for the corresponding base $SB$ is 8.89 units.

Formula for the Area of triangle, $A= \frac{1}{2}(base\times height)$

So, the area of the $\triangle SBA$ will be: $\frac{1}{2}(\sqrt{1130}\times 8.89)= 149.42... \approx 149$ square units. (Rounded to the nearest unit)

3 0

3 years ago

A bag contains marbles numbered 1 through 100. Zoe draws a marble. Then, without replacing the marble, she draws a second marble

Neporo4naja [7]

If starting out, there are 100 marbles and Zoe pulls out a 5 and doesn't replace it, then there are 99 marbles left to choose from. So, there are 9 digits 1-10 (not including #5) making the proportion you have left 9/99 which simplifies to 1/11

6 0

3 years ago