Answer:
105.46 feet
Step-by-step explanation:
We know all three angles (60, 90, and 30), as well as one side, which is adjacent to the 60 degrees. We want to find the side opposite to the 60 degree angle. To do this, we can use tangent, utilizing both opposite and adjacent.
Using tan, we can say that tan(60) = x/58, with x representing the height of the lighthouse (minus 5, because Santos is 5 feet tall and he is measuring the angle from the top of his head). Multiplying both sides by 58, we can get that 58 *tan(60) = x = 100.46. Add 5 to that to get 105.46 feet as your answer.
(10x^2 - 8x - 1) + (4x^2 - 8x - 5) = 10x^2 - 8x - 1 + 4x^2 - 8x - 5 = 14x^2 - 16x - 6
and since we know now what "x", let's use that in either equation, say the first equation,
another way to do it is by "elimination", depending on the equations, one way may work quicker than the other, in this case, substitution was the simpler one, because the first equation is already solved for "y", so we just grabbed it and plugged it in the 2nd equation.
