|20 points.
joshua has a ladder that is 17 ft long. he wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5 ft above the ground. for safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. will the ladder be safe at this height? show your work.

No. The ladder is too steep.

Step-by-step explanation:

Length of ladder = 17 feet.  This is the hypotenuse.

Side a of a right triangle = 16.6

To answer this, you need one of the trigonometric functions.  

Opposite = 16.5

hypotenuse = 17

The function you need is the sine function.

Sin(theta) = opposite / hypotenuse

sin(theta) = 16.5 / 17

Sin(theta) = 0.97059

theta = sin-1(0.07059)

theta = 76.07

No the ladder is too steep.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl