Ask question

Ask question

All categories

4 years ago

15

Joshua has a ladder that is 12 ft long. He will lean the ladder against a vertical wall. For safety reasons, he wants the angle

the ladder makes with the ground to be no greater than 75°. Is it possible for Joshua to lean the ladder against the wall so that the top of the ladder is at least 11.8 ft above the ground?

1 answer:

xenn [34]4 years ago

8 0

We first determine the height that the top of the ladder will reach given that the angle to be made is no greater than 75°. In the right triangle formed, the hypotenuse is 12. The trigonometric function that is derived from the scenario is,
x = (sin 75°)(12 ft) = 11.59 ft
Thus, the highest point that the ladder will reach should only be approximately equal to 11.59 ft.

You might be interested in

Ava wants to draw a parallelogram on the coordinate plane. She

wolverine [178]

Answer:

$k =(2,1)$

$JK = 2$

Step-by-step explanation:

Given

$J = (0,1)$ ---- $(x_1,y_1)$

$H = (1,-2)$ --- $(x_2,y_2)$

$I = (3,-2)$ --- $(x_3,y_3)$

See attachment for grid

Solving (a): The coordinates of K

The parallelogram has the following diagonals: IJ and HK

Diagonals bisect one another. So:

Midpoint of IJ = Midpoint of HK

This gives:

$\frac{1}{2}(I + J) = \frac{1}{2}(H+K)$

$\frac{1}{2}(x_3+x_1,y_3+y_1) = \frac{1}{2}(x_2+x,y_2+y)$

$\frac{1}{2}(3+0,-2+1) = \frac{1}{2}(1+x,-2+y)$

$\frac{1}{2}(3,-1) = \frac{1}{2}(1+x,-2+y)$

Multiply through by 2

$(3,-1) = (1+x,-2+y)$

By comparison:

$1 + x = 3$

$-2 + y = -1$

Solve for x and y

$x = 3 - 1 =2$

$y = -1 +2 = 1$

So, the coordinates of k is:

$k =(2,1)$

The length of JK is calculated using distance (d) formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

$J = (0,1)$ ---- $(x_1,y_1)$

$k =(2,1)$ ---- $(x_2,y_2)$

So:

$d = \sqrt{(0 - 2)^2 + (1 - 1)^2$

$d = \sqrt{(- 2)^2 + (0)^2$

$d = \sqrt{4 + 0$

$d = \sqrt{4$

$d = 2$

Hence:

$JK = 2$

8 0

3 years ago

olga_2 [115]

Step-by-step explanation:

$(7r+5s)^2$

use the pattern

$(a+b)^2=a^2+2ab+b^2$

$(7r+5s)^2=(7r+5s)(7r+5s)$

Apply FOIL method to multiply the parenthesis

$(7r+5s)^2=(7r+5s)(7r+5s)$

$(7r+5s)(7r+5s)\\49r^2+35rs+35rs+25s^2\\49r^2+70rs+25s^2$

Compare the expression with $(a+b)^2=a^2+2ab+b^2$

The value of a=7r and the value of b=5s

Answer :

a=7r , b=5s

4 0

3 years ago

What is √180 * 2√30 simplified?

Alex73 [517]

√180 x 2√30
√36 x 5 x 2√30
6√5 x 2√30
12√5 x √30
12√5 x 30
12√150
12√25 x 6
12 x 5√6
60√6

8 0

3 years ago

Given the function f (x) = - x^2 + 8x + 9 state whether the vertex represents a maximum or minimum point for the function explai

Marta_Voda [28]

The vertex will be a maximum because the equation is negative, meaning the parabola opens downwards and will have a maximum point but no minimum point as it will get infinitely smaller.

3 0

3 years ago

PLEASE HELP!!!!<br>how to solve 9x^3-16x^2=0 by factoring<br> WILL GIVE BRAINLIEST IF CORRECT!!!!

andreev551 [17]

Answer:

x=5.3

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

x

≈

5.3

Hope this helps, can you now give me brainliest??

7 0

3 years ago