A playground slide is 14.5 feet long with an 8.5-foot tall ladder. What is the measure of the angle that the slide makes with th
e ground, x, to the nearest degree?
2 answers:
The slide and the ladder made a right angle triangle with the ground. The angle that the slide made with the ground is labeled as 
in the diagram below. We can use the trigonometry ratio to work out the size of the angle.
8.3 is the side opposite to the angle and 14.5 is the hypotenuse. We need to use the Sin ratio
° to the nearest degree
8.3 is the side opposite to the angle and 14.5 is the hypotenuse. We need to use the Sin ratio
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Answer:
There are two possibilities:
and
and
Step-by-step explanation:
Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:
First, is cleared in the first equation:
Now, the variable is substituted in the second one:
And some algebra is done in order to simplify the expression:
Roots are found by means of the General Equation for Second-Order Polynomials:
and
There are two different values for :
There are two possibilities:
and
and