Trig question?

Question

A road with an angle of inclination greater than 4.5 degrees is considered steep for trucks. A road rises 65m in a horizontal distance of 540m. Is the road considered steep? Explain

My answer:
is 6.9 degrees i used sin

Is this right ???

Answer 1

You are absolutely correct!

I used tangent, you used sine which implies you had to use the Pythagorean theorem to determine the hypotenuse, which is OK if you want to solve it in that manner.

arc tan x = 65/540

x = 6.86°
.

Answer 2

Because the question was "Is the road steep?", the answer is "Yes". This is because the angle of inclination is 6.9 degrees; however, you should be using tan because you know the opposite side which is 65m and the adjacent side which is 540m. The tan of the angle is the length of the opposite side divided by the length of the adjacent side.

Answer 3

first step is to set up the triangle so you can visualize it. draw a right triangle with run being much longer than the rise. label the run (horizontal side) as 540m and the rise (vertical size) as 65m. now label the angle inbetween these two sides as x. this is what we are trying to find. from this information, we can say tanx=65m/540m because tangentis the opposite over the adjacent. take an inverse tangent of both sides so we get x= inversetan(65/540). plug this into your graphing calculator and you will get the measure of the angle of the road. hope this helps!