anginih86

2022-06-24

The problem is: Given parallelogram ABCD with diagonals $\overline{\mathrm{A}\mathrm{C}}$ and $\overline{\mathrm{B}\mathrm{D}}$ intersecting at E. If m$\mathrm{\angle}\text{}AEB$=60 degrees, m$\mathrm{\angle}\text{}CAB$=30 degrees, and AB=18, find AD.

This problem seems simple, and I presume that you use the properties of special right triangles; however, I can't seem to get the right answer. The answer is 6 $\sqrt{\text{}}21$. Thank you!

This problem seems simple, and I presume that you use the properties of special right triangles; however, I can't seem to get the right answer. The answer is 6 $\sqrt{\text{}}21$. Thank you!

Amy Daniels

Beginner2022-06-25Added 20 answers

Since $\measuredangle ABE={90}^{\circ}$, we obtain

$BE=18\mathrm{tan}{30}^{\circ}=6\sqrt{3},$

which gives

$BD=12\sqrt{3}.$

Thus,

$AD=\sqrt{{18}^{2}+{\left(12\sqrt{3}\right)}^{2}}=\sqrt{756}=6\sqrt{21}.$

$BE=18\mathrm{tan}{30}^{\circ}=6\sqrt{3},$

which gives

$BD=12\sqrt{3}.$

Thus,

$AD=\sqrt{{18}^{2}+{\left(12\sqrt{3}\right)}^{2}}=\sqrt{756}=6\sqrt{21}.$

The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola $A)\frac{\sqrt{5}}{4}\phantom{\rule{0ex}{0ex}}B)\frac{\sqrt{7}}{4}\phantom{\rule{0ex}{0ex}}C)\frac{7}{4}\phantom{\rule{0ex}{0ex}}D)\frac{5}{3}$

Which of the following is an example of a pair of parallel lines?

Sides of a triangle

Surface of a ball

Corner of a room

Railway trackState whether the statements are True or False. All rectangles are parallelograms.

Point T(3, −8) is reflected across the x-axis. Which statements about T' are true?

If two parallel lines are cut by a transversal, then:

each pair of alternate angles are equal

each pair of alternate angles add up to 180 degrees

each pair of corresponding angles add up to 180 degees.

each pair of corresponding angles is equal.The opposite faces of a dice always have a total of ___ on them.

What is the term for a part of a line with two endpoints?

A. Line Segment

B. Line

C. Ray

D. PointABCD is a parallelogram. Which of the following is not true about ABCD?

AB=CD

AD=CB

AD||CD

AB||CDIf the points $(a,0)$, $(0,b)$ and $(1,1)$ are collinear then which of the following is true?

$\frac{1}{a}+\frac{1}{b}=1$

$\frac{1}{a}-\frac{1}{b}=2$

$\frac{1}{a}-\frac{1}{b}=-1$

$\frac{1}{a}+\frac{1}{b}=2$The angles of a triangle are in the ratio 1 : 1 : 2. What is the largest angle in the triangle?

$A){90}^{\circ}\phantom{\rule{0ex}{0ex}}B){135}^{\circ}\phantom{\rule{0ex}{0ex}}C){45}^{\circ}\phantom{\rule{0ex}{0ex}}D){150}^{\circ}$What is the greatest number of acute angles that a triangle can contain?

How many right angles are required to create a complete angle?

1) Two

2) Three

3) Four

4) FiveFind the sum of interior angles of a polygon with 12 sides in degrees.${1800}^{\circ}\phantom{\rule{0ex}{0ex}}{1200}^{\circ}\phantom{\rule{0ex}{0ex}}{1500}^{\circ}\phantom{\rule{0ex}{0ex}}{1400}^{\circ}$

In Euclid's Division Lemma when $a=bq+r$ where $a,b$ are positive integers then what values $r$ can take?

When two lines cross each other at a point we call them ___ lines.