Find the missing b for a trapezoid with a=68, h=4, b=21

1 answer:

4 0

We will have to use the formula for the area of a trapezoid on this problem, which is ( $b_1$ and $b_2$ are the bases of the trapezoid and $h$ is the height):

$\dfrac{b_1 + b_2}{2} \cdot h$

All we need to do is substitute the information we are given into our formula:

$\dfrac{21 + b_2}{2} \cdot 4 = 68$

Now, let's just simplify the equation:

$\dfrac{21 + b_2}{2} \cdot 4 = 68$

$\dfrac{21 + b_2}{2} = 17$

$21 + b_2 = 34$

$b_2 = 13$

The missing base has a length of 13 units.

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In the diagram of circle o, what is the measure of ABC? 27° 54° 108° 120°

Vlad1618 [11]

Given:

Given that a circle O with two tangents BA and BC.

The major arc AC is 234°

The minor arc AC is 126°

We need to determine the measure of ∠ABC

Measure of ∠ABC:

We know the property that, "if a tangent and a secant, two tangents or two secants intersect in the interior of the circle, then the measure of angle formed is one half the difference of the measures of the intercepted arcs."

Hence, applying the above property, we have;

$\angle ABC=\frac{1}{2}( major \widehat{AC} - minor \widehat{AC})$