The tangent of an angle is the ratio of the adjacent side over the opposite side.
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For this case we have that by definition, the area of a triangle is given by:
Where:
b: It is the base of the triangle
h: It is the height of the triangle
According to the statement data we have:
Substituting we have:
We divide between 2 on both sides:
We factor by looking for two numbers that, when multiplied, are obtained -88 and when added together, +3 is obtained.
These numbers are +11 and -8.
We have two roots:
We choose the positive value.
Thus, the base of the triangle is:
Answer:
The base of the triangle is 22 units.
To find the area of the shaded region, we must first find the percentage that is shaded.
We understand that 140 degrees out of 360 degrees are unshaded, thus there are 220 degrees shaded.
Thus the percentage is equal to
Area = square yards
Hope that helps!