Given GH is tangent to ⊙T at N. If m∠ANG = 54°, what is mAB ? A circle with centre T is given. GH is tangent to the circle
which touches the circumference of the circle at point N. From N, a diameter NTB is drawn. A chord AN is also given, this chord forms an acute angle with tangent. mAB = 72 °
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To answer this question, you should draw it out- see the attached picture for the example. All the side lengths are labeled. You can then use the area of a trapezoid formula to find the total area.
A=1/2 (b1 + b2)h
You can see the substitution for each value in the work shown in the picture.
A=1/2 (b1 + b2)h
You can see the substitution for each value in the work shown in the picture.
When the ball will hit the ground, the height will be zero. So we need to replace 
with 0 in our equation, and solve for 
:
To solve this equation we are going to use the quadratic formula:
.
From our height equation, we can infer that
, 
, and 
. So lets replace those values in our quadratic formula to find
or 
or 
Since time cannot be negative, is the solution of our equation.
We can conclude that the ball will hit the ground after 2.71 seconds.
To solve this equation we are going to use the quadratic formula:
From our height equation, we can infer that
Since time cannot be negative,
We can conclude that the ball will hit the ground after 2.71 seconds.