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Alex787 [66]
3 years ago
8

In △ABC, m∠ACB=90°, m∠ACD=60°, CD is the altitude to AB , and BD = 5 cm. Find AD.

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
5 0

Answer:

5cm

Step-by-step explanation:

Find the diagram attached.

From ΔBCD, ∠BCD = 90-∠ACD

∠BCD = 90-60

∠BCD = 30°

Also tan60 = CD/BD

tan 60 = CD/5

CD = 5tan60

CD = 5√3 cm

Similarly from ΔACD, tan30 = CD/AD

tan30 = 5√3/AD

AD = 5√3/tan30

AD =  5√3/(1/√3)

AD = 5√3 * √3/1

AD = 5 cm

Hence the length of side AD is 5cm

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Solve for x and graph the solution on the number line below.

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Multiply both sides by - 1 (reverse the inequality)$(-x)(-1) \leq 6(-1)$

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$-x-5+5 < -8+5$

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Multiply both sides by $-1$ (reversing the inequality)

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1 year ago
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The ratio of AC/AB is given by

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3 years ago
Which conic section does this equation represent?
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8 0
3 years ago
Read 2 more answers
Company A offers a starting salary of $28,000 with a raise of $3,000 each year. Company B offers a starting salary of $36,000 wi
8090 [49]
Starting salary offered by Company A = $28000
Amount of raise per year given by Company A per year = $3000
Starting salary offered by Company B =$36000
Amount of raise per year given by Company B = $2000
Let us assume the number of years after which the salary offered by Company A will be the same as Company B = x
Then
28000 + 3000x = 36000 + 2000x
3000x - 2000x = 36000 - 28000
1000x = 8000
x = 8000/1000
   = 8 years
So from the above deduction we can conclude that after 8 years the salary of Company A and Company B will become equal.
More information's are also provided for the second part of the question.
Starting salary offered by Company C = $18000
Let us assume the amount of raise per year given by Company C = z dollars
Number of years in which the salaries of Company C will become equal to the salaries of Company A and B = 8 years
Then
18000 + 8z = 28000 + (3000 * 8)
18000 + 8z = 28000 + 24000
18000 + 8z = 52000
8z = 52000 - 18000
8z = 34000
z = 34000/8
   = 4250 dollars
From the above deduction we can conclude that the raise given by Company C should be $4250.
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3 years ago
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[1 / 8] ÷ [3 / 4] 

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<span>So, [1 / 8] ÷ [3 / 4] = [1 / 8] × [4 / 3] </span>

<span>From there, multiply as you would normally. Then reduce it to lowest terms. </span>

<span>4 / 24 = 1 / 6 </span>

<span>Therefore, the answer is 1 / 6.</span>
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