Mathematics, 16.12.2019 18:31, esta54

Given: △авс, m∠acb = 90° cd ⊥ ab , m∠acd = 30°, ac = 8 cm find: bd

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answered: adenn3693

In the diagram ΔABC, ∠ACB = 90°, CD⊥AB, ∠ACD = 30°, AC = 8 cm.

Suppose BD = x and CD = y.

If angle ∠ACD = 30°, then angle ∠BCD = 60°

and angle ∠CAD = 60°, angle ∠CBD = 30°

Now we have two small right triangle ΔCDA and ΔCDB.

In Right Triangle ΔCDA; AC = 8 cm and ∠ACD = 30°.

$cos(30^o) = \frac{CD}{AC} \\CD = AC*cos(30^o)\\y = 8*\frac{\sqrt{3}} {2} \\y = 4\sqrt{3}$

In Right Triangle ΔCDB; angle ∠BCD = 60° and CD = y = 4√3.

$tan(60^o) = \frac{BD}{CD} \\BD = CD*tan(60^o) \\x = y* \sqrt{3} \\x = 4\sqrt{3} *\sqrt{3} \\x = 4*3\\x=12 \;cm$

Hence, BD = 12 cm.

Given: △авс, m∠acb = 90° cd ⊥ ab , m∠acd = 30°, ac = 8 cm find: bd

answered: hella33revj

Length of BD = 20,784 cm

Further ExplanationThe first step, find the length of the CB

AC length known = 8 cm

sin 30 ° = AC / CB

1/2 = 8 / CB

CB = 1/2 * 8

CB = 16 cm

Then find the length of the CB

sin 60 ° = CB / BA

1/2 sqrt 3 = 16 / BA

BA = 1/2 sqrt 3 * 16

BA = 13,856 cm

Then find the length of the CD

sin 90 ° = AC / CD

1 = 8 / CD

CD = 1 * 8

CD = 8 cm

And the last one is looking for DA length

sin 60 ° = CD / DA

1/2 sqrt 3 = 8 / DA

DA = 1/2 sqrt 3 * 8

DA = 6,928 cm

So, the length of BD is BA + AD = 13,856 + 6,928 = 20,784 cm

A triangle is the name of a shape made from three sides in the form of a straight line and three angles. The mathematician Euclid who lived around 300 BC found that the sum of the three angles on a triangle on a flat plane was 180° degrees. This allows us to calculate the magnitude of one angle when the other two angles are known.

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Triangle Formula link

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Class: Middle/High School and College

Subject: Mathematics

Keyword: degrees, angles, triangle

answered: Guest

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ a(\stackrel{x_1}{5}~,~\stackrel{y_1}{4})\qquad b(\stackrel{x_2}{x}~,~\stackrel{y_2}{y})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{ab}{7}=\sqrt{(x-5)^2+(y-4)^2}~\hfill$

answered: Guest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.