You have a prepaid bus pass that has $10 on it. Every time you ride the bus it costs you 50 cents. Assume that you cannot put an
ymore money on the card after it is used. Create an equation for the situation above.
1 answer:
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Answer:
Step-by-step explanation:
We can use the trigonometric formula for the area of a triangle:
Where a and b are the side lengths, and C is the angle <em>between</em> the two side lengths.
As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.
We will determine the area of each triangle individually and then sum their values.
Right Triangle ABD:
We can use the above area formula if we know the angle between two sides.
Looking at our triangle, we know that ∠ADB is 55 DB is 10.
So, if we can find AD, we can apply the formula.
Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.
Since this is a right triangle, we can utilize the trig ratios.
In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.
Therefore:
Solve for AD:
Now, we can use the formula. We have:
Substituting AD for a, 10 for b, and 55 for C, we get:
Simplify. Therefore, the area of the right triangle is:
We will not evaluate this, as we do not want inaccuracies in our final answer.
Scalene Triangle CDB:
We will use the same tactic as above.
We see that if we can determine CD, we can use our area formula.
First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:
Notice that we know the angle opposite to CD.
And, ∠C is opposite to BD, which measures 10.
Therefore, we can use the Law of Sines to determine CD:
Where A and B are the angles opposite to its respective sides.
So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:
Solve for CD. Cross-multiply:
Divide both sides by sin(98). Hence:
Therefore, we can now use our area formula:
We will substitute 10 for a, CD for b, and 44 for C. Hence:
Simplify. So, the area of the scalene triangle is:
Therefore, our total area will be given by:
Approximate. Use a calculator. Thus:
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